Bibliographic Cross-References
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Intuitionistic Logic Explorer Bibliographic Cross-References |
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| Bibliographic Reference | Description | Intuitionistic Logic Explorer Page(s) |
|---|---|---|
| [AczelRathjen], p. 71 | Definition 8.1.4 | enumct 7448 fidcenum 7266 |
| [AczelRathjen], p. 72 | Proposition 8.1.11 | fidcenum 7266 |
| [AczelRathjen], p. 73 | Lemma 8.1.14 | enumct 7448 |
| [AczelRathjen], p. 73 | Corollary 8.1.13 | ennnfone 13297 |
| [AczelRathjen], p. 74 | Lemma 8.1.16 | xpfi 7232 |
| [AczelRathjen], p. 74 | Remark 8.1.17 | unfiexmid 7218 |
| [AczelRathjen], p. 74 | Theorem 8.1.19 | ctiunct 13312 |
| [AczelRathjen], p. 75 | Corollary 8.1.20 | unct 13314 |
| [AczelRathjen], p. 75 | Corollary 8.1.23 | qnnen 13303 znnen 13270 |
| [AczelRathjen], p. 77 | Lemma 8.1.27 | omctfn 13315 |
| [AczelRathjen], p. 78 | Theorem 8.1.28 | omiunct 13316 |
| [AczelRathjen], p. 80 | Corollary 8.2.4 | df-ihash 11196 |
| [AczelRathjen], p. 183 | Chapter 20 | ax-setind 4682 |
| [AhoHopUll] p. 318 | Section 9.1 | df-concat 11340 df-pfx 11426 df-substr 11399 df-word 11286 lencl 11289 wrd0 11310 |
| [Apostol] p. 18 | Theorem I.1 | addcan 8499 addcan2d 8504 addcan2i 8502 addcand 8503 addcani 8501 |
| [Apostol] p. 18 | Theorem I.2 | negeu 8510 |
| [Apostol] p. 18 | Theorem I.3 | negsub 8567 negsubd 8636 negsubi 8597 |
| [Apostol] p. 18 | Theorem I.4 | negneg 8569 negnegd 8621 negnegi 8589 |
| [Apostol] p. 18 | Theorem I.5 | subdi 8705 subdid 8734 subdii 8727 subdir 8706 subdird 8735 subdiri 8728 |
| [Apostol] p. 18 | Theorem I.6 | mul01 8709 mul01d 8713 mul01i 8711 mul02 8707 mul02d 8712 mul02i 8710 |
| [Apostol] p. 18 | Theorem I.9 | divrecapd 9116 |
| [Apostol] p. 18 | Theorem I.10 | recrecapi 9067 |
| [Apostol] p. 18 | Theorem I.12 | mul2neg 8718 mul2negd 8733 mul2negi 8726 mulneg1 8715 mulneg1d 8731 mulneg1i 8724 |
| [Apostol] p. 18 | Theorem I.14 | rdivmuldivd 14427 |
| [Apostol] p. 18 | Theorem I.15 | divdivdivap 9036 |
| [Apostol] p. 20 | Axiom 7 | rpaddcl 10060 rpaddcld 10095 rpmulcl 10061 rpmulcld 10096 |
| [Apostol] p. 20 | Axiom 9 | 0nrp 10072 |
| [Apostol] p. 20 | Theorem I.17 | lttri 8423 |
| [Apostol] p. 20 | Theorem I.18 | ltadd1d 8859 ltadd1dd 8877 ltadd1i 8823 |
| [Apostol] p. 20 | Theorem I.19 | ltmul1 8913 ltmul1a 8912 ltmul1i 9243 ltmul1ii 9251 ltmul2 9179 ltmul2d 10122 ltmul2dd 10136 ltmul2i 9246 |
| [Apostol] p. 20 | Theorem I.21 | 0lt1 8446 |
| [Apostol] p. 20 | Theorem I.23 | lt0neg1 8789 lt0neg1d 8836 ltneg 8783 ltnegd 8844 ltnegi 8814 |
| [Apostol] p. 20 | Theorem I.25 | lt2add 8766 lt2addd 8888 lt2addi 8831 |
| [Apostol] p. 20 | Definition of positive numbers | df-rp 10037 |
| [Apostol] p. 21 | Exercise 4 | recgt0 9173 recgt0d 9257 recgt0i 9229 recgt0ii 9230 |
| [Apostol] p. 22 | Definition of integers | df-z 9627 |
| [Apostol] p. 22 | Definition of rationals | df-q 10002 |
| [Apostol] p. 24 | Theorem I.26 | supeuti 7327 |
| [Apostol] p. 26 | Theorem I.29 | arch 9542 |
| [Apostol] p. 28 | Exercise 2 | btwnz 9747 |
| [Apostol] p. 28 | Exercise 3 | nnrecl 9543 |
| [Apostol] p. 28 | Exercise 6 | qbtwnre 10672 |
| [Apostol] p. 28 | Exercise 10(a) | zeneo 12619 zneo 9729 |
| [Apostol] p. 29 | Theorem I.35 | resqrtth 11778 sqrtthi 11866 |
| [Apostol] p. 34 | Theorem I.36 (principle of mathematical induction) | peano5nni 9289 |
| [Apostol] p. 34 | Theorem I.37 (well-ordering principle) | nnwodc 12794 |
| [Apostol] p. 363 | Remark | absgt0api 11893 |
| [Apostol] p. 363 | Example | abssubd 11940 abssubi 11897 |
| [ApostolNT] p. 14 | Definition | df-dvds 12536 |
| [ApostolNT] p. 14 | Theorem 1.1(a) | iddvds 12552 |
| [ApostolNT] p. 14 | Theorem 1.1(b) | dvdstr 12576 |
| [ApostolNT] p. 14 | Theorem 1.1(c) | dvds2ln 12572 |
| [ApostolNT] p. 14 | Theorem 1.1(d) | dvdscmul 12566 |
| [ApostolNT] p. 14 | Theorem 1.1(e) | dvdscmulr 12568 |
| [ApostolNT] p. 14 | Theorem 1.1(f) | 1dvds 12553 |
| [ApostolNT] p. 14 | Theorem 1.1(g) | dvds0 12554 |
| [ApostolNT] p. 14 | Theorem 1.1(h) | 0dvds 12559 |
| [ApostolNT] p. 14 | Theorem 1.1(i) | dvdsleabs 12593 |
| [ApostolNT] p. 14 | Theorem 1.1(j) | dvdsabseq 12595 |
| [ApostolNT] p. 14 | Theorem 1.1(k) | divconjdvds 12597 |
| [ApostolNT] p. 15 | Definition | dfgcd2 12772 |
| [ApostolNT] p. 16 | Definition | isprm2 12876 |
| [ApostolNT] p. 16 | Theorem 1.5 | coprmdvds 12851 |
| [ApostolNT] p. 16 | Theorem 1.7 | prminf 13327 |
| [ApostolNT] p. 16 | Theorem 1.4(a) | gcdcom 12731 |
| [ApostolNT] p. 16 | Theorem 1.4(b) | gcdass 12773 |
| [ApostolNT] p. 16 | Theorem 1.4(c) | absmulgcd 12775 |
| [ApostolNT] p. 16 | Theorem 1.4(d)1 | gcd1 12745 |
| [ApostolNT] p. 16 | Theorem 1.4(d)2 | gcdid0 12738 |
| [ApostolNT] p. 17 | Theorem 1.8 | coprm 12903 |
| [ApostolNT] p. 17 | Theorem 1.9 | euclemma 12905 |
| [ApostolNT] p. 17 | Theorem 1.10 | 1arith2 13128 |
| [ApostolNT] p. 19 | Theorem 1.14 | divalg 12672 |
| [ApostolNT] p. 20 | Theorem 1.15 | eucalg 12818 |
| [ApostolNT] p. 25 | Definition | df-phi 12970 |
| [ApostolNT] p. 26 | Theorem 2.2 | phisum 13000 |
| [ApostolNT] p. 28 | Theorem 2.5(a) | phiprmpw 12981 |
| [ApostolNT] p. 28 | Theorem 2.5(c) | phimul 12985 |
| [ApostolNT] p. 38 | Remark | df-sgm 16013 |
| [ApostolNT] p. 38 | Definition | df-sgm 16013 |
| [ApostolNT] p. 104 | Definition | congr 12859 |
| [ApostolNT] p. 106 | Remark | dvdsval3 12539 |
| [ApostolNT] p. 106 | Definition | moddvds 12547 |
| [ApostolNT] p. 107 | Example 2 | mod2eq0even 12626 |
| [ApostolNT] p. 107 | Example 3 | mod2eq1n2dvds 12627 |
| [ApostolNT] p. 107 | Example 4 | zmod1congr 10759 |
| [ApostolNT] p. 107 | Theorem 5.2(b) | modqmul12d 10796 |
| [ApostolNT] p. 107 | Theorem 5.2(c) | modqexp 11085 |
| [ApostolNT] p. 108 | Theorem 5.3 | modmulconst 12571 |
| [ApostolNT] p. 109 | Theorem 5.4 | cncongr1 12862 |
| [ApostolNT] p. 109 | Theorem 5.6 | gcdmodi 13181 |
| [ApostolNT] p. 109 | Theorem 5.4 "Cancellation law" | cncongr 12864 |
| [ApostolNT] p. 113 | Theorem 5.17 | eulerth 12992 |
| [ApostolNT] p. 113 | Theorem 5.18 | vfermltl 13011 |
| [ApostolNT] p. 114 | Theorem 5.19 | fermltl 12993 |
| [ApostolNT] p. 179 | Definition | df-lgs 16034 lgsprme0 16078 |
| [ApostolNT] p. 180 | Example 1 | 1lgs 16079 |
| [ApostolNT] p. 180 | Theorem 9.2 | lgsvalmod 16055 |
| [ApostolNT] p. 180 | Theorem 9.3 | lgsdirprm 16070 |
| [ApostolNT] p. 181 | Theorem 9.4 | m1lgs 16121 |
| [ApostolNT] p. 181 | Theorem 9.5 | 2lgs 16140 2lgsoddprm 16149 |
| [ApostolNT] p. 182 | Theorem 9.6 | gausslemma2d 16105 |
| [ApostolNT] p. 185 | Theorem 9.8 | lgsquad 16116 |
| [ApostolNT] p. 188 | Definition | df-lgs 16034 lgs1 16080 |
| [ApostolNT] p. 188 | Theorem 9.9(a) | lgsdir 16071 |
| [ApostolNT] p. 188 | Theorem 9.9(b) | lgsdi 16073 |
| [ApostolNT] p. 188 | Theorem 9.9(c) | lgsmodeq 16081 |
| [ApostolNT] p. 188 | Theorem 9.9(d) | lgsmulsqcoprm 16082 |
| [Bauer] p. 482 | Section 1.2 | pm2.01 625 pm2.65 669 |
| [Bauer] p. 483 | Theorem 1.3 | acexmid 6077 onsucelsucexmidlem 4674 |
| [Bauer], p. 481 | Section 1.1 | pwtrufal 16944 |
| [Bauer], p. 483 | Definition | n0rf 3534 |
| [Bauer], p. 483 | Theorem 1.2 | 2irrexpq 16004 2irrexpqap 16006 |
| [Bauer], p. 485 | Theorem 2.1 | exmidssfi 7239 ssfiexmid 7171 ssfiexmidt 7173 |
| [Bauer], p. 493 | Section 5.1 | ivthdich 15680 |
| [Bauer], p. 494 | Theorem 5.5 | ivthinc 15670 |
| [BauerHanson], p. 27 | Proposition 5.2 | cnstab 8966 |
| [BauerSwan], p. 3 | Definition on page 14:3 | enumct 7448 |
| [BauerSwan], p. 14 | Remark | 0ct 7440 ctm 7442 |
| [BauerSwan], p. 14 | Proposition 2.6 | subctctexmid 16947 |
| [BauerTaylor], p. 32 | Lemma 6.16 | prarloclem 7861 |
| [BauerTaylor], p. 50 | Lemma 11.4 | subhalfnqq 7774 |
| [BauerTaylor], p. 52 | Proposition 11.15 | prarloc 7863 |
| [BauerTaylor], p. 53 | Lemma 11.16 | addclpr 7897 addlocpr 7896 |
| [BauerTaylor], p. 55 | Proposition 12.7 | appdivnq 7923 |
| [BauerTaylor], p. 56 | Lemma 12.8 | prmuloc 7926 |
| [BauerTaylor], p. 56 | Lemma 12.9 | mullocpr 7931 |
| [BellMachover] p. 36 | Lemma 10.3 | idALT 20 |
| [BellMachover] p. 97 | Definition 10.1 | df-eu 2089 |
| [BellMachover] p. 460 | Notation | df-mo 2090 |
| [BellMachover] p. 460 | Definition | mo3 2141 mo3h 2140 |
| [BellMachover] p. 462 | Theorem 1.1 | bm1.1 2223 |
| [BellMachover] p. 463 | Theorem 1.3ii | bm1.3ii 4252 |
| [BellMachover] p. 466 | Axiom Pow | axpow3 4312 |
| [BellMachover] p. 466 | Axiom Union | axun2 4578 |
| [BellMachover] p. 469 | Theorem 2.2(i) | ordirr 4687 |
| [BellMachover] p. 469 | Theorem 2.2(iii) | onelon 4527 |
| [BellMachover] p. 469 | Theorem 2.2(vii) | ordn2lp 4690 |
| [BellMachover] p. 471 | Problem 2.5(ii) | bm2.5ii 4641 |
| [BellMachover] p. 471 | Definition of Lim | df-ilim 4512 |
| [BellMachover] p. 472 | Axiom Inf | zfinf2 4734 |
| [BellMachover] p. 473 | Theorem 2.8 | limom 4759 |
| [Bobzien] p. 116 | Statement T3 | stoic3 1480 |
| [Bobzien] p. 117 | Statement T2 | stoic2a 1478 |
| [Bobzien] p. 117 | Statement T4 | stoic4a 1481 |
| [Bobzien] p. 117 | Conclusion the contradictory | stoic1a 1476 |
| [Bollobas] p. 1 | Section I.1 | df-edg 16216 isuhgropm 16239 isusgropen 16323 isuspgropen 16322 |
| [Bollobas] p. 2 | Section I.1 | df-subgr 16412 uhgrspansubgr 16435 |
| [Bollobas] p. 4 | Definition | df-wlks 16476 |
| [Bollobas] p. 5 | Definition | df-trls 16539 |
| [Bollobas] p. 7 | Section I.1 | df-ushgrm 16228 |
| [BourbakiAlg1] p. 1 | Definition 1 | df-mgm 13656 |
| [BourbakiAlg1] p. 4 | Definition 5 | df-sgrp 13697 |
| [BourbakiAlg1] p. 12 | Definition 2 | df-mnd 13710 |
| [BourbakiAlg1] p. 92 | Definition 1 | df-ring 14279 |
| [BourbakiAlg1] p. 93 | Section I.8.1 | df-rng 14210 |
| [BourbakiEns] p. | Proposition 8 | fcof1 5982 fcofo 5983 |
| [BourbakiTop1] p. | Remark | xnegmnf 10213 xnegpnf 10212 |
| [BourbakiTop1] p. | Remark | rexneg 10214 |
| [BourbakiTop1] p. | Proposition | ishmeo 15331 |
| [BourbakiTop1] p. | Property V_i | ssnei2 15184 |
| [BourbakiTop1] p. | Property V_ii | innei 15190 |
| [BourbakiTop1] p. | Property V_iv | neissex 15192 |
| [BourbakiTop1] p. | Proposition 1 | neipsm 15181 neiss 15177 |
| [BourbakiTop1] p. | Proposition 2 | cnptopco 15249 |
| [BourbakiTop1] p. | Proposition 4 | imasnopn 15326 |
| [BourbakiTop1] p. | Property V_iii | elnei 15179 |
| [BourbakiTop1] p. | Definition is due to Bourbaki (Def. 1 | df-top 15025 |
| [Bruck] p. 1 | Section I.1 | df-mgm 13656 |
| [Bruck] p. 23 | Section II.1 | df-sgrp 13697 |
| [Bruck] p. 28 | Theorem 3.2 | dfgrp3m 13884 |
| [ChoquetDD] p. 2 | Definition of mapping | df-mpt 4192 |
| [Church] p. 129 | Section II.24 | df-ifp 991 dfifp2dc 994 |
| [Cohen] p. 301 | Remark | relogoprlem 15895 |
| [Cohen] p. 301 | Property 2 | relogmul 15896 relogmuld 15911 |
| [Cohen] p. 301 | Property 3 | relogdiv 15897 relogdivd 15912 |
| [Cohen] p. 301 | Property 4 | relogexp 15899 |
| [Cohen] p. 301 | Property 1a | log1 15893 |
| [Cohen] p. 301 | Property 1b | loge 15894 |
| [Cohen4] p. 348 | Observation | relogbcxpbap 15993 |
| [Cohen4] p. 352 | Definition | rpelogb 15977 |
| [Cohen4] p. 361 | Property 2 | rprelogbmul 15983 |
| [Cohen4] p. 361 | Property 3 | logbrec 15988 rprelogbdiv 15985 |
| [Cohen4] p. 361 | Property 4 | rplogbreexp 15981 |
| [Cohen4] p. 361 | Property 6 | relogbexpap 15986 |
| [Cohen4] p. 361 | Property 1(a) | rplogbid1 15975 |
| [Cohen4] p. 361 | Property 1(b) | rplogb1 15976 |
| [Cohen4] p. 367 | Property | rplogbchbase 15978 |
| [Cohen4] p. 377 | Property 2 | logblt 15990 |
| [Crosilla] p. | Axiom 1 | ax-ext 2220 |
| [Crosilla] p. | Axiom 2 | ax-pr 4344 |
| [Crosilla] p. | Axiom 3 | ax-un 4576 |
| [Crosilla] p. | Axiom 4 | ax-nul 4257 |
| [Crosilla] p. | Axiom 5 | ax-iinf 4733 |
| [Crosilla] p. | Axiom 6 | ru 3050 |
| [Crosilla] p. | Axiom 8 | ax-pow 4309 |
| [Crosilla] p. | Axiom 9 | ax-setind 4682 |
| [Crosilla], p. | Axiom 6 | ax-sep 4247 |
| [Crosilla], p. | Axiom 7 | ax-coll 4244 |
| [Crosilla], p. | Axiom 7' | repizf 4245 |
| [Crosilla], p. | Theorem is stated | ordtriexmid 4666 |
| [Crosilla], p. | Axiom of choice implies instances | acexmid 6077 |
| [Crosilla], p. | Definition of ordinal | df-iord 4509 |
| [Crosilla], p. | Theorem "Foundation implies instances of EM" | regexmid 4680 |
| [Diestel] p. 4 | Section 1.1 | df-subgr 16412 uhgrspansubgr 16435 |
| [Diestel] p. 27 | Section 1.10 | df-ushgrm 16228 |
| [Eisenberg] p. 67 | Definition 5.3 | df-dif 3222 |
| [Eisenberg] p. 82 | Definition 6.3 | df-iom 4736 |
| [Eisenberg] p. 125 | Definition 8.21 | df-map 6917 |
| [Enderton] p. 18 | Axiom of Empty Set | axnul 4256 |
| [Enderton] p. 19 | Definition | df-tp 3716 |
| [Enderton] p. 26 | Exercise 5 | unissb 3963 |
| [Enderton] p. 26 | Exercise 10 | pwel 4356 |
| [Enderton] p. 28 | Exercise 7(b) | pwunim 4429 |
| [Enderton] p. 30 | Theorem "Distributive laws" | iinin1m 4080 iinin2m 4079 iunin1 4075 iunin2 4074 |
| [Enderton] p. 31 | Theorem "De Morgan's laws" | iindif2m 4078 iundif2ss 4076 |
| [Enderton] p. 33 | Exercise 23 | iinuniss 4093 |
| [Enderton] p. 33 | Exercise 25 | iununir 4094 |
| [Enderton] p. 33 | Exercise 24(a) | iinpw 4101 |
| [Enderton] p. 33 | Exercise 24(b) | iunpw 4624 iunpwss 4102 |
| [Enderton] p. 38 | Exercise 6(a) | unipw 4355 |
| [Enderton] p. 38 | Exercise 6(b) | pwuni 4327 |
| [Enderton] p. 41 | Lemma 3D | opeluu 4594 rnex 5048 rnexg 5045 |
| [Enderton] p. 41 | Exercise 8 | dmuni 4989 rnuni 5197 |
| [Enderton] p. 42 | Definition of a function | dffun7 5402 dffun8 5403 |
| [Enderton] p. 43 | Definition of function value | funfvdm2 5764 |
| [Enderton] p. 43 | Definition of single-rooted | funcnv 5440 |
| [Enderton] p. 44 | Definition (d) | dfima2 5126 dfima3 5127 |
| [Enderton] p. 47 | Theorem 3H | fvco2 5771 |
| [Enderton] p. 49 | Axiom of Choice (first form) | df-ac 7555 |
| [Enderton] p. 50 | Theorem 3K(a) | imauni 5960 |
| [Enderton] p. 52 | Definition | df-map 6917 |
| [Enderton] p. 53 | Exercise 21 | coass 5304 |
| [Enderton] p. 53 | Exercise 27 | dmco 5294 |
| [Enderton] p. 53 | Exercise 14(a) | funin 5450 |
| [Enderton] p. 53 | Exercise 22(a) | imass2 5161 |
| [Enderton] p. 54 | Remark | ixpf 6995 ixpssmap 7007 |
| [Enderton] p. 54 | Definition of infinite Cartesian product | df-ixp 6974 |
| [Enderton] p. 56 | Theorem 3M | erref 6820 |
| [Enderton] p. 57 | Lemma 3N | erthi 6848 |
| [Enderton] p. 57 | Definition | df-ec 6802 |
| [Enderton] p. 58 | Definition | df-qs 6806 |
| [Enderton] p. 60 | Theorem 3Q | th3q 6907 th3qcor 6906 th3qlem1 6904 th3qlem2 6905 |
| [Enderton] p. 61 | Exercise 35 | df-ec 6802 |
| [Enderton] p. 65 | Exercise 56(a) | dmun 4986 |
| [Enderton] p. 68 | Definition of successor | df-suc 4514 |
| [Enderton] p. 71 | Definition | df-tr 4228 dftr4 4232 |
| [Enderton] p. 72 | Theorem 4E | unisuc 4556 unisucg 4557 |
| [Enderton] p. 73 | Exercise 6 | unisuc 4556 unisucg 4557 |
| [Enderton] p. 73 | Exercise 5(a) | truni 4241 |
| [Enderton] p. 73 | Exercise 5(b) | trint 4242 |
| [Enderton] p. 79 | Theorem 4I(A1) | nna0 6740 |
| [Enderton] p. 79 | Theorem 4I(A2) | nnasuc 6742 onasuc 6732 |
| [Enderton] p. 79 | Definition of operation value | df-ov 6081 |
| [Enderton] p. 80 | Theorem 4J(A1) | nnm0 6741 |
| [Enderton] p. 80 | Theorem 4J(A2) | nnmsuc 6743 onmsuc 6739 |
| [Enderton] p. 81 | Theorem 4K(1) | nnaass 6751 |
| [Enderton] p. 81 | Theorem 4K(2) | nna0r 6744 nnacom 6750 |
| [Enderton] p. 81 | Theorem 4K(3) | nndi 6752 |
| [Enderton] p. 81 | Theorem 4K(4) | nnmass 6753 |
| [Enderton] p. 81 | Theorem 4K(5) | nnmcom 6755 |
| [Enderton] p. 82 | Exercise 16 | nnm0r 6745 nnmsucr 6754 |
| [Enderton] p. 88 | Exercise 23 | nnaordex 6794 |
| [Enderton] p. 129 | Definition | df-en 7016 |
| [Enderton] p. 132 | Theorem 6B(b) | canth 6029 |
| [Enderton] p. 133 | Exercise 1 | xpomen 13267 |
| [Enderton] p. 134 | Theorem (Pigeonhole Principle) | phpm 7160 |
| [Enderton] p. 136 | Corollary 6E | nneneq 7151 |
| [Enderton] p. 139 | Theorem 6H(c) | mapen 7139 |
| [Enderton] p. 142 | Theorem 6I(3) | xpdjuen 7567 |
| [Enderton] p. 143 | Theorem 6J | dju0en 7563 dju1en 7562 |
| [Enderton] p. 144 | Corollary 6K | undif2ss 3603 |
| [Enderton] p. 145 | Figure 38 | ffoss 5670 |
| [Enderton] p. 145 | Definition | df-dom 7017 |
| [Enderton] p. 146 | Example 1 | domen 7028 domeng 7029 |
| [Enderton] p. 146 | Example 3 | nndomo 7158 |
| [Enderton] p. 149 | Theorem 6L(c) | xpdom1 7126 xpdom1g 7124 xpdom2g 7123 |
| [Enderton] p. 168 | Definition | df-po 4439 |
| [Enderton] p. 192 | Theorem 7M(a) | oneli 4571 |
| [Enderton] p. 192 | Theorem 7M(b) | ontr1 4532 |
| [Enderton] p. 192 | Theorem 7M(c) | onirri 4688 |
| [Enderton] p. 193 | Corollary 7N(b) | 0elon 4535 |
| [Enderton] p. 193 | Corollary 7N(c) | onsuci 4661 |
| [Enderton] p. 193 | Corollary 7N(d) | ssonunii 4634 |
| [Enderton] p. 194 | Remark | onprc 4697 |
| [Enderton] p. 194 | Exercise 16 | suc11 4703 |
| [Enderton] p. 197 | Definition | df-card 7517 |
| [Enderton] p. 200 | Exercise 25 | tfis 4728 |
| [Enderton] p. 206 | Theorem 7X(b) | en2lp 4699 |
| [Enderton] p. 207 | Exercise 34 | opthreg 4701 |
| [Enderton] p. 208 | Exercise 35 | suc11g 4702 |
| [Geuvers], p. 1 | Remark | expap0 10987 |
| [Geuvers], p. 6 | Lemma 2.13 | mulap0r 8936 |
| [Geuvers], p. 6 | Lemma 2.15 | mulap0 8975 |
| [Geuvers], p. 9 | Lemma 2.35 | msqge0 8937 |
| [Geuvers], p. 9 | Definition 3.1(2) | ax-arch 8291 |
| [Geuvers], p. 10 | Lemma 3.9 | maxcom 11950 |
| [Geuvers], p. 10 | Lemma 3.10 | maxle1 11958 maxle2 11959 |
| [Geuvers], p. 10 | Lemma 3.11 | maxleast 11960 |
| [Geuvers], p. 10 | Lemma 3.12 | maxleb 11963 |
| [Geuvers], p. 11 | Definition 3.13 | dfabsmax 11964 |
| [Geuvers], p. 17 | Definition 6.1 | df-ap 8903 |
| [Gleason] p. 117 | Proposition 9-2.1 | df-enq 7707 enqer 7718 |
| [Gleason] p. 117 | Proposition 9-2.2 | df-1nqqs 7711 df-nqqs 7708 |
| [Gleason] p. 117 | Proposition 9-2.3 | df-plpq 7704 df-plqqs 7709 |
| [Gleason] p. 119 | Proposition 9-2.4 | df-mpq 7705 df-mqqs 7710 |
| [Gleason] p. 119 | Proposition 9-2.5 | df-rq 7712 |
| [Gleason] p. 119 | Proposition 9-2.6 | ltexnqq 7768 |
| [Gleason] p. 120 | Proposition 9-2.6(i) | halfnq 7771 ltbtwnnq 7776 ltbtwnnqq 7775 |
| [Gleason] p. 120 | Proposition 9-2.6(ii) | ltanqg 7760 |
| [Gleason] p. 120 | Proposition 9-2.6(iii) | ltmnqg 7761 |
| [Gleason] p. 123 | Proposition 9-3.5 | addclpr 7897 |
| [Gleason] p. 123 | Proposition 9-3.5(i) | addassprg 7939 |
| [Gleason] p. 123 | Proposition 9-3.5(ii) | addcomprg 7938 |
| [Gleason] p. 123 | Proposition 9-3.5(iii) | ltaddpr 7957 |
| [Gleason] p. 123 | Proposition 9-3.5(iv) | ltexpri 7973 |
| [Gleason] p. 123 | Proposition 9-3.5(v) | ltaprg 7979 ltaprlem 7978 |
| [Gleason] p. 123 | Proposition 9-3.5(vi) | addcanprg 7976 |
| [Gleason] p. 124 | Proposition 9-3.7 | mulclpr 7932 |
| [Gleason] p. 124 | Theorem 9-3.7(iv) | 1idpr 7952 |
| [Gleason] p. 124 | Proposition 9-3.7(i) | mulassprg 7941 |
| [Gleason] p. 124 | Proposition 9-3.7(ii) | mulcomprg 7940 |
| [Gleason] p. 124 | Proposition 9-3.7(iii) | distrprg 7948 |
| [Gleason] p. 124 | Proposition 9-3.7(v) | recexpr 7998 |
| [Gleason] p. 126 | Proposition 9-4.1 | df-enr 8086 enrer 8095 |
| [Gleason] p. 126 | Proposition 9-4.2 | df-0r 8091 df-1r 8092 df-nr 8087 |
| [Gleason] p. 126 | Proposition 9-4.3 | df-mr 8089 df-plr 8088 negexsr 8132 recexsrlem 8134 |
| [Gleason] p. 127 | Proposition 9-4.4 | df-ltr 8090 |
| [Gleason] p. 130 | Proposition 10-1.3 | creui 9283 creur 9282 cru 8923 |
| [Gleason] p. 130 | Definition 10-1.1(v) | ax-cnre 8283 axcnre 8241 |
| [Gleason] p. 132 | Definition 10-3.1 | crim 11604 crimd 11724 crimi 11684 crre 11603 crred 11723 crrei 11683 |
| [Gleason] p. 132 | Definition 10-3.2 | remim 11606 remimd 11689 |
| [Gleason] p. 133 | Definition 10.36 | absval2 11804 absval2d 11932 absval2i 11891 |
| [Gleason] p. 133 | Proposition 10-3.4(a) | cjadd 11630 cjaddd 11712 cjaddi 11679 |
| [Gleason] p. 133 | Proposition 10-3.4(c) | cjmul 11631 cjmuld 11713 cjmuli 11680 |
| [Gleason] p. 133 | Proposition 10-3.4(e) | cjcj 11629 cjcjd 11690 cjcji 11662 |
| [Gleason] p. 133 | Proposition 10-3.4(f) | cjre 11628 cjreb 11612 cjrebd 11693 cjrebi 11665 cjred 11718 rere 11611 rereb 11609 rerebd 11692 rerebi 11664 rered 11716 |
| [Gleason] p. 133 | Proposition 10-3.4(h) | addcj 11637 addcjd 11704 addcji 11674 |
| [Gleason] p. 133 | Proposition 10-3.7(a) | absval 11748 |
| [Gleason] p. 133 | Proposition 10-3.7(b) | abscj 11799 abscjd 11937 abscji 11895 |
| [Gleason] p. 133 | Proposition 10-3.7(c) | abs00 11811 abs00d 11933 abs00i 11892 absne0d 11934 |
| [Gleason] p. 133 | Proposition 10-3.7(d) | releabs 11843 releabsd 11938 releabsi 11896 |
| [Gleason] p. 133 | Proposition 10-3.7(f) | absmul 11816 absmuld 11941 absmuli 11898 |
| [Gleason] p. 133 | Proposition 10-3.7(g) | sqabsadd 11802 sqabsaddi 11899 |
| [Gleason] p. 133 | Proposition 10-3.7(h) | abstri 11851 abstrid 11943 abstrii 11902 |
| [Gleason] p. 134 | Definition 10-4.1 | df-exp 10957 exp0 10961 expp1 10964 expp1d 11093 |
| [Gleason] p. 135 | Proposition 10-4.2(a) | expadd 10999 expaddd 11094 |
| [Gleason] p. 135 | Proposition 10-4.2(b) | cxpmul 15940 cxpmuld 15965 expmul 11002 expmuld 11095 |
| [Gleason] p. 135 | Proposition 10-4.2(c) | mulexp 10996 mulexpd 11107 rpmulcxp 15937 |
| [Gleason] p. 141 | Definition 11-2.1 | fzval 10395 |
| [Gleason] p. 168 | Proposition 12-2.1(a) | climadd 12073 |
| [Gleason] p. 168 | Proposition 12-2.1(b) | climsub 12075 |
| [Gleason] p. 168 | Proposition 12-2.1(c) | climmul 12074 |
| [Gleason] p. 171 | Corollary 12-2.2 | climmulc2 12078 |
| [Gleason] p. 172 | Corollary 12-2.5 | climrecl 12071 |
| [Gleason] p. 172 | Proposition 12-2.4(c) | climabs 12067 climcj 12068 climim 12070 climre 12069 |
| [Gleason] p. 173 | Definition 12-3.1 | df-ltxr 8358 df-xr 8357 ltxr 10159 |
| [Gleason] p. 180 | Theorem 12-5.3 | climcau 12094 |
| [Gleason] p. 217 | Lemma 13-4.1 | btwnzge0 10716 |
| [Gleason] p. 223 | Definition 14-1.1 | df-met 14857 |
| [Gleason] p. 223 | Definition 14-1.1(a) | met0 15391 xmet0 15390 |
| [Gleason] p. 223 | Definition 14-1.1(c) | metsym 15398 |
| [Gleason] p. 223 | Definition 14-1.1(d) | mettri 15400 mstri 15500 xmettri 15399 xmstri 15499 |
| [Gleason] p. 230 | Proposition 14-2.6 | txlm 15306 |
| [Gleason] p. 240 | Proposition 14-4.2 | metcnp3 15538 |
| [Gleason] p. 243 | Proposition 14-4.16 | addcn2 12057 addcncntop 15589 mulcn2 12059 mulcncntop 15591 subcn2 12058 subcncntop 15590 |
| [Gleason] p. 295 | Remark | bcval3 11170 bcval4 11171 |
| [Gleason] p. 295 | Equation 2 | bcpasc 11185 |
| [Gleason] p. 295 | Definition of binomial coefficient | bcval 11168 df-bc 11167 |
| [Gleason] p. 296 | Remark | bcn0 11174 bcnn 11176 |
| [Gleason] p. 296 | Theorem 15-2.8 | binom 12232 |
| [Gleason] p. 308 | Equation 2 | ef0 12420 |
| [Gleason] p. 308 | Equation 3 | efcj 12421 |
| [Gleason] p. 309 | Corollary 15-4.3 | efne0 12426 |
| [Gleason] p. 309 | Corollary 15-4.4 | efexp 12430 |
| [Gleason] p. 310 | Equation 14 | sinadd 12484 |
| [Gleason] p. 310 | Equation 15 | cosadd 12485 |
| [Gleason] p. 311 | Equation 17 | sincossq 12496 |
| [Gleason] p. 311 | Equation 18 | cosbnd 12501 sinbnd 12500 |
| [Gleason] p. 311 | Definition of ` ` | df-pi 12401 |
| [Golan] p. 1 | Remark | srgisid 14267 |
| [Golan] p. 1 | Definition | df-srg 14245 |
| [Hamilton] p. 31 | Example 2.7(a) | idALT 20 |
| [Hamilton] p. 73 | Rule 1 | ax-mp 5 |
| [Hamilton] p. 74 | Rule 2 | ax-gen 1502 |
| [Herstein] p. 55 | Lemma 2.2.1(a) | grpideu 13796 mndideu 13719 |
| [Herstein] p. 55 | Lemma 2.2.1(b) | grpinveu 13823 |
| [Herstein] p. 55 | Lemma 2.2.1(c) | grpinvinv 13852 |
| [Herstein] p. 55 | Lemma 2.2.1(d) | grpinvadd 13863 |
| [Herstein] p. 57 | Exercise 1 | dfgrp3me 13885 |
| [Heyting] p. 127 | Axiom #1 | ax1hfs 17032 |
| [Hitchcock] p. 5 | Rule A3 | mptnan 1472 |
| [Hitchcock] p. 5 | Rule A4 | mptxor 1473 |
| [Hitchcock] p. 5 | Rule A5 | mtpxor 1475 |
| [HoTT], p. | Lemma 10.4.1 | exmidontriim 7574 |
| [HoTT], p. | Theorem 7.2.6 | nndceq 6765 |
| [HoTT], p. | Exercise 11.10 | neapmkv 17026 |
| [HoTT], p. | Exercise 11.11 | mulap0bd 8978 |
| [HoTT], p. | Section 11.2.1 | df-iltp 7830 df-imp 7829 df-iplp 7828 df-reap 8896 |
| [HoTT], p. | Theorem 11.2.4 | recapb 8994 rerecapb 9166 |
| [HoTT], p. | Corollary 3.9.2 | uchoice 6364 |
| [HoTT], p. | Theorem 11.2.12 | cauappcvgpr 8022 |
| [HoTT], p. | Corollary 11.4.3 | conventions 16652 |
| [HoTT], p. | Exercise 11.6(i) | dcapnconst 17019 dceqnconst 17018 |
| [HoTT], p. | Corollary 11.2.13 | axcaucvg 8260 caucvgpr 8042 caucvgprpr 8072 caucvgsr 8162 |
| [HoTT], p. | Definition 11.2.1 | df-inp 7826 |
| [HoTT], p. | Exercise 11.6(ii) | nconstwlpo 17024 |
| [HoTT], p. | Proposition 11.2.3 | df-iso 4440 ltpopr 7955 ltsopr 7956 |
| [HoTT], p. | Definition 11.2.7(v) | apsym 8927 reapcotr 8919 reapirr 8898 |
| [HoTT], p. | Definition 11.2.7(vi) | 0lt1 8446 gt0add 8894 leadd1 8751 lelttr 8407 lemul1a 9181 lenlt 8394 ltadd1 8750 ltletr 8408 ltmul1 8913 reaplt 8909 |
| [Huneke] p. 2 | Statement | df-clwwlknon 16585 |
| [Jech] p. 4 | Definition of class | cv 1401 cvjust 2233 |
| [Jech] p. 78 | Note | opthprc 4824 |
| [KalishMontague] p. 81 | Note 1 | ax-i9 1583 |
| [Kreyszig] p. 3 | Property M1 | metcl 15380 xmetcl 15379 |
| [Kreyszig] p. 4 | Property M2 | meteq0 15387 |
| [Kreyszig] p. 12 | Equation 5 | muleqadd 8991 |
| [Kreyszig] p. 18 | Definition 1.3-2 | mopnval 15469 |
| [Kreyszig] p. 19 | Remark | mopntopon 15470 |
| [Kreyszig] p. 19 | Theorem T1 | mopn0 15515 mopnm 15475 |
| [Kreyszig] p. 19 | Theorem T2 | unimopn 15513 |
| [Kreyszig] p. 19 | Definition of neighborhood | neibl 15518 |
| [Kreyszig] p. 20 | Definition 1.3-3 | metcnp2 15540 |
| [Kreyszig] p. 25 | Definition 1.4-1 | lmbr 15240 |
| [Kreyszig] p. 51 | Equation 2 | lmodvneg1 14642 |
| [Kreyszig] p. 51 | Equation 1a | lmod0vs 14633 |
| [Kreyszig] p. 51 | Equation 1b | lmodvs0 14634 |
| [Kunen] p. 10 | Axiom 0 | a9e 1748 |
| [Kunen] p. 12 | Axiom 6 | zfrep6 4246 |
| [Kunen] p. 24 | Definition 10.24 | mapval 6927 mapvalg 6925 |
| [Kunen] p. 31 | Definition 10.24 | mapex 6921 |
| [KuratowskiMostowski] p. 109 | Section. Eq. 14 | iuniin 4020 |
| [Lang] p. 3 | Statement | lidrideqd 13681 mndbn0 13724 |
| [Lang] p. 3 | Definition | df-mnd 13710 |
| [Lang] p. 4 | Definition of a (finite) product | gzsumsplit1r 13695 |
| [Lang] p. 5 | Equation | gzsumreidx 14121 |
| [Lang] p. 6 | Definition | mulgnn0gzsum 13911 |
| [Lang] p. 7 | Definition | dfgrp2e 13813 |
| [Levy] p. 338 | Axiom | df-clab 2225 df-clel 2234 df-cleq 2231 |
| [Lopez-Astorga] p. 12 | Rule 1 | mptnan 1472 |
| [Lopez-Astorga] p. 12 | Rule 2 | mptxor 1473 |
| [Lopez-Astorga] p. 12 | Rule 3 | mtpxor 1475 |
| [Margaris] p. 40 | Rule C | exlimiv 1651 |
| [Margaris] p. 49 | Axiom A1 | ax-1 6 |
| [Margaris] p. 49 | Axiom A2 | ax-2 7 |
| [Margaris] p. 49 | Axiom A3 | condc 865 |
| [Margaris] p. 49 | Definition | dfbi2 392 dfordc 904 exalim 1555 |
| [Margaris] p. 51 | Theorem 1 | idALT 20 |
| [Margaris] p. 56 | Theorem 3 | syld 45 |
| [Margaris] p. 60 | Theorem 8 | jcn 661 |
| [Margaris] p. 89 | Theorem 19.2 | 19.2 1691 r19.2m 3614 |
| [Margaris] p. 89 | Theorem 19.3 | 19.3 1607 19.3h 1606 rr19.3v 2965 |
| [Margaris] p. 89 | Theorem 19.5 | alcom 1531 |
| [Margaris] p. 89 | Theorem 19.6 | alexdc 1672 alexim 1698 |
| [Margaris] p. 89 | Theorem 19.7 | alnex 1552 |
| [Margaris] p. 89 | Theorem 19.8 | 19.8a 1643 spsbe 1895 |
| [Margaris] p. 89 | Theorem 19.9 | 19.9 1697 19.9h 1696 19.9v 1924 exlimd 1650 |
| [Margaris] p. 89 | Theorem 19.11 | excom 1716 excomim 1715 |
| [Margaris] p. 89 | Theorem 19.12 | 19.12 1717 r19.12 2657 |
| [Margaris] p. 90 | Theorem 19.14 | exnalim 1699 |
| [Margaris] p. 90 | Theorem 19.15 | albi 1521 ralbi 2683 |
| [Margaris] p. 90 | Theorem 19.16 | 19.16 1608 |
| [Margaris] p. 90 | Theorem 19.17 | 19.17 1609 |
| [Margaris] p. 90 | Theorem 19.18 | exbi 1657 rexbi 2684 |
| [Margaris] p. 90 | Theorem 19.19 | 19.19 1718 |
| [Margaris] p. 90 | Theorem 19.20 | alim 1510 alimd 1574 alimdh 1520 alimdv 1932 ralimdaa 2616 ralimdv 2618 ralimdva 2617 ralimdvva 2619 sbcimdv 3117 |
| [Margaris] p. 90 | Theorem 19.21 | 19.21-2 1719 19.21 1636 19.21bi 1611 19.21h 1610 19.21ht 1634 19.21t 1635 19.21v 1926 alrimd 1663 alrimdd 1662 alrimdh 1532 alrimdv 1929 alrimi 1575 alrimih 1522 alrimiv 1927 alrimivv 1928 r19.21 2626 r19.21be 2641 r19.21bi 2638 r19.21t 2625 r19.21v 2627 ralrimd 2628 ralrimdv 2629 ralrimdva 2630 ralrimdvv 2634 ralrimdvva 2635 ralrimi 2621 ralrimiv 2622 ralrimiva 2623 ralrimivv 2631 ralrimivva 2632 ralrimivvva 2633 ralrimivw 2624 rexlimi 2661 |
| [Margaris] p. 90 | Theorem 19.22 | 2alimdv 1934 2eximdv 1935 exim 1652 eximd 1665 eximdh 1664 eximdv 1933 rexim 2644 reximdai 2648 reximddv 2653 reximddv2 2655 reximdv 2651 reximdv2 2649 reximdva 2652 reximdvai 2650 reximi2 2646 |
| [Margaris] p. 90 | Theorem 19.23 | 19.23 1730 19.23bi 1645 19.23h 1551 19.23ht 1550 19.23t 1729 19.23v 1936 19.23vv 1937 exlimd2 1648 exlimdh 1649 exlimdv 1872 exlimdvv 1953 exlimi 1647 exlimih 1646 exlimiv 1651 exlimivv 1952 r19.23 2659 r19.23v 2660 rexlimd 2665 rexlimdv 2667 rexlimdv3a 2670 rexlimdva 2668 rexlimdva2 2671 rexlimdvaa 2669 rexlimdvv 2675 rexlimdvva 2676 rexlimdvw 2672 rexlimiv 2662 rexlimiva 2663 rexlimivv 2674 |
| [Margaris] p. 90 | Theorem 19.24 | i19.24 1692 |
| [Margaris] p. 90 | Theorem 19.25 | 19.25 1679 |
| [Margaris] p. 90 | Theorem 19.26 | 19.26-2 1535 19.26-3an 1536 19.26 1534 r19.26-2 2680 r19.26-3 2681 r19.26 2677 r19.26m 2682 |
| [Margaris] p. 90 | Theorem 19.27 | 19.27 1614 19.27h 1613 19.27v 1955 r19.27av 2686 r19.27m 3623 r19.27mv 3624 |
| [Margaris] p. 90 | Theorem 19.28 | 19.28 1616 19.28h 1615 19.28v 1956 r19.28av 2687 r19.28m 3617 r19.28mv 3620 rr19.28v 2966 |
| [Margaris] p. 90 | Theorem 19.29 | 19.29 1673 19.29r 1674 19.29r2 1675 19.29x 1676 r19.29 2688 r19.29d2r 2695 r19.29r 2689 |
| [Margaris] p. 90 | Theorem 19.30 | 19.30dc 1680 |
| [Margaris] p. 90 | Theorem 19.31 | 19.31r 1733 |
| [Margaris] p. 90 | Theorem 19.32 | 19.32dc 1731 19.32r 1732 r19.32r 2697 r19.32vdc 2700 r19.32vr 2699 |
| [Margaris] p. 90 | Theorem 19.33 | 19.33 1537 19.33b2 1682 19.33bdc 1683 |
| [Margaris] p. 90 | Theorem 19.34 | 19.34 1736 |
| [Margaris] p. 90 | Theorem 19.35 | 19.35-1 1677 19.35i 1678 |
| [Margaris] p. 90 | Theorem 19.36 | 19.36-1 1725 19.36aiv 1957 19.36i 1724 r19.36av 2702 |
| [Margaris] p. 90 | Theorem 19.37 | 19.37-1 1726 19.37aiv 1727 r19.37 2703 r19.37av 2704 |
| [Margaris] p. 90 | Theorem 19.38 | 19.38 1728 |
| [Margaris] p. 90 | Theorem 19.39 | i19.39 1693 |
| [Margaris] p. 90 | Theorem 19.40 | 19.40-2 1685 19.40 1684 r19.40 2705 |
| [Margaris] p. 90 | Theorem 19.41 | 19.41 1738 19.41h 1737 19.41v 1958 19.41vv 1959 19.41vvv 1960 19.41vvvv 1961 r19.41 2706 r19.41v 2707 |
| [Margaris] p. 90 | Theorem 19.42 | 19.42 1740 19.42h 1739 19.42v 1962 19.42vv 1967 19.42vvv 1968 19.42vvvv 1969 r19.42v 2708 |
| [Margaris] p. 90 | Theorem 19.43 | 19.43 1681 r19.43 2709 |
| [Margaris] p. 90 | Theorem 19.44 | 19.44 1734 r19.44av 2710 r19.44mv 3622 |
| [Margaris] p. 90 | Theorem 19.45 | 19.45 1735 r19.45av 2711 r19.45mv 3621 |
| [Margaris] p. 110 | Exercise 2(b) | eu1 2111 |
| [Megill] p. 444 | Axiom C5 | ax-17 1579 |
| [Megill] p. 445 | Lemma L12 | alequcom 1568 ax-10 1558 |
| [Megill] p. 446 | Lemma L17 | equtrr 1762 |
| [Megill] p. 446 | Lemma L19 | hbnae 1773 |
| [Megill] p. 447 | Remark 9.1 | df-sb 1816 sbid 1827 |
| [Megill] p. 448 | Scheme C5' | ax-4 1563 |
| [Megill] p. 448 | Scheme C6' | ax-7 1501 |
| [Megill] p. 448 | Scheme C8' | ax-8 1557 |
| [Megill] p. 448 | Scheme C9' | ax-i12 1560 |
| [Megill] p. 448 | Scheme C11' | ax-10o 1768 |
| [Megill] p. 448 | Scheme C12' | ax-13 2211 |
| [Megill] p. 448 | Scheme C13' | ax-14 2212 |
| [Megill] p. 448 | Scheme C15' | ax-11o 1876 |
| [Megill] p. 448 | Scheme C16' | ax-16 1867 |
| [Megill] p. 448 | Theorem 9.4 | dral1 1783 dral2 1784 drex1 1851 drex2 1785 drsb1 1852 drsb2 1894 |
| [Megill] p. 449 | Theorem 9.7 | sbcom2 2047 sbequ 1893 sbid2v 2056 |
| [Megill] p. 450 | Example in Appendix | hba1 1593 |
| [Mendelson] p. 36 | Lemma 1.8 | idALT 20 |
| [Mendelson] p. 69 | Axiom 4 | rspsbc 3135 rspsbca 3136 stdpc4 1828 |
| [Mendelson] p. 69 | Axiom 5 | ra5 3141 stdpc5 1637 |
| [Mendelson] p. 81 | Rule C | exlimiv 1651 |
| [Mendelson] p. 95 | Axiom 6 | stdpc6 1755 |
| [Mendelson] p. 95 | Axiom 7 | stdpc7 1823 |
| [Mendelson] p. 231 | Exercise 4.10(k) | inv1 3559 |
| [Mendelson] p. 231 | Exercise 4.10(l) | unv 3560 |
| [Mendelson] p. 231 | Exercise 4.10(n) | inssun 3471 |
| [Mendelson] p. 231 | Exercise 4.10(o) | df-nul 3521 |
| [Mendelson] p. 231 | Exercise 4.10(q) | inssddif 3472 |
| [Mendelson] p. 231 | Exercise 4.10(s) | ddifnel 3360 |
| [Mendelson] p. 231 | Definition of union | unssin 3470 |
| [Mendelson] p. 235 | Exercise 4.12(c) | univ 4620 |
| [Mendelson] p. 235 | Exercise 4.12(d) | pwv 3932 |
| [Mendelson] p. 235 | Exercise 4.12(j) | pwin 4425 |
| [Mendelson] p. 235 | Exercise 4.12(k) | pwunss 4426 |
| [Mendelson] p. 235 | Exercise 4.12(l) | pwssunim 4427 |
| [Mendelson] p. 235 | Exercise 4.12(n) | uniin 3953 |
| [Mendelson] p. 235 | Exercise 4.12(p) | reli 4907 |
| [Mendelson] p. 235 | Exercise 4.12(t) | relssdmrn 5306 |
| [Mendelson] p. 246 | Definition of successor | df-suc 4514 |
| [Mendelson] p. 254 | Proposition 4.22(b) | xpen 7138 |
| [Mendelson] p. 254 | Proposition 4.22(c) | xpsnen 7112 xpsneng 7113 |
| [Mendelson] p. 254 | Proposition 4.22(d) | xpcomen 7118 xpcomeng 7119 |
| [Mendelson] p. 254 | Proposition 4.22(e) | xpassen 7121 |
| [Mendelson] p. 255 | Exercise 4.39 | endisj 7115 |
| [Mendelson] p. 255 | Exercise 4.41 | mapprc 6919 |
| [Mendelson] p. 255 | Exercise 4.43 | mapsnen 7093 mapsnend 7092 |
| [Mendelson] p. 255 | Exercise 4.45 | mapunen 7144 |
| [Mendelson] p. 255 | Exercise 4.47 | xpmapen 7143 |
| [Mendelson] p. 255 | Exercise 4.42(a) | map0e 6960 |
| [Mendelson] p. 255 | Exercise 4.42(b) | map1 7094 |
| [Mendelson] p. 258 | Exercise 4.56(c) | djuassen 7566 djucomen 7565 |
| [Mendelson] p. 258 | Exercise 4.56(g) | xp2dju 7564 |
| [Mendelson] p. 266 | Proposition 4.34(a) | oa1suc 6733 |
| [Monk1] p. 26 | Theorem 2.8(vii) | ssin 3453 |
| [Monk1] p. 33 | Theorem 3.2(i) | ssrel 4861 |
| [Monk1] p. 33 | Theorem 3.2(ii) | eqrel 4862 |
| [Monk1] p. 34 | Definition 3.3 | df-opab 4191 |
| [Monk1] p. 36 | Theorem 3.7(i) | coi1 5301 coi2 5302 |
| [Monk1] p. 36 | Theorem 3.8(v) | dm0 4993 rn0 5036 |
| [Monk1] p. 36 | Theorem 3.7(ii) | cnvi 5190 |
| [Monk1] p. 37 | Theorem 3.13(i) | relxp 4882 |
| [Monk1] p. 37 | Theorem 3.13(x) | dmxpm 5000 rnxpm 5215 |
| [Monk1] p. 37 | Theorem 3.13(ii) | 0xp 4853 xp0 5205 |
| [Monk1] p. 38 | Theorem 3.16(ii) | ima0 5144 |
| [Monk1] p. 38 | Theorem 3.16(viii) | imai 5141 |
| [Monk1] p. 39 | Theorem 3.17 | imaex 5139 imaexg 5138 |
| [Monk1] p. 39 | Theorem 3.16(xi) | imassrn 5135 |
| [Monk1] p. 41 | Theorem 4.3(i) | fnopfv 5832 funfvop 5815 |
| [Monk1] p. 42 | Theorem 4.3(ii) | funopfvb 5741 |
| [Monk1] p. 42 | Theorem 4.4(iii) | fvelima 5751 |
| [Monk1] p. 43 | Theorem 4.6 | funun 5420 |
| [Monk1] p. 43 | Theorem 4.8(iv) | dff13 5967 dff13f 5969 |
| [Monk1] p. 46 | Theorem 4.15(v) | funex 5934 funrnex 6336 |
| [Monk1] p. 50 | Definition 5.4 | fniunfv 5961 |
| [Monk1] p. 52 | Theorem 5.12(ii) | op2ndb 5269 |
| [Monk1] p. 52 | Theorem 5.11(viii) | ssint 3984 |
| [Monk1] p. 52 | Definition 5.13 (i) | 1stval2 6382 df-1st 6367 |
| [Monk1] p. 52 | Definition 5.13 (ii) | 2ndval2 6383 df-2nd 6368 |
| [Monk2] p. 105 | Axiom C4 | ax-5 1500 |
| [Monk2] p. 105 | Axiom C7 | ax-8 1557 |
| [Monk2] p. 105 | Axiom C8 | ax-11 1559 ax-11o 1876 |
| [Monk2] p. 105 | Axiom (C8) | ax11v 1880 |
| [Monk2] p. 109 | Lemma 12 | ax-7 1501 |
| [Monk2] p. 109 | Lemma 15 | equvin 1916 equvini 1811 eqvinop 4381 |
| [Monk2] p. 113 | Axiom C5-1 | ax-17 1579 |
| [Monk2] p. 113 | Axiom C5-2 | hbn1 1704 |
| [Monk2] p. 113 | Axiom C5-3 | ax-7 1501 |
| [Monk2] p. 114 | Lemma 22 | hba1 1593 |
| [Monk2] p. 114 | Lemma 23 | hbia1 1605 nfia1 1633 |
| [Monk2] p. 114 | Lemma 24 | hba2 1604 nfa2 1632 |
| [Moschovakis] p. 2 | Chapter 2 | df-stab 843 dftest 17033 |
| [Munkres] p. 77 | Example 2 | distop 15112 |
| [Munkres] p. 78 | Definition of basis | df-bases 15070 isbasis3g 15073 |
| [Munkres] p. 78 | Definition of a topology generated by a basis | df-topgen 13594 tgval2 15078 |
| [Munkres] p. 79 | Remark | tgcl 15091 |
| [Munkres] p. 80 | Lemma 2.1 | tgval3 15085 |
| [Munkres] p. 80 | Lemma 2.2 | tgss2 15106 tgss3 15105 |
| [Munkres] p. 81 | Lemma 2.3 | basgen 15107 basgen2 15108 |
| [Munkres] p. 89 | Definition of subspace topology | resttop 15197 |
| [Munkres] p. 93 | Theorem 6.1(1) | 0cld 15139 topcld 15136 |
| [Munkres] p. 93 | Theorem 6.1(3) | uncld 15140 |
| [Munkres] p. 94 | Definition of closure | clsval 15138 |
| [Munkres] p. 94 | Definition of interior | ntrval 15137 |
| [Munkres] p. 102 | Definition of continuous function | df-cn 15215 iscn 15224 iscn2 15227 |
| [Munkres] p. 107 | Theorem 7.2(g) | cncnp 15257 cncnp2m 15258 cncnpi 15255 df-cnp 15216 iscnp 15226 |
| [Munkres] p. 127 | Theorem 10.1 | metcn 15541 |
| [Pierik], p. 8 | Section 2.2.1 | dfrex2fin 7201 |
| [Pierik], p. 9 | Definition 2.4 | df-womni 7497 |
| [Pierik], p. 9 | Definition 2.5 | df-markov 7485 omniwomnimkv 7500 |
| [Pierik], p. 10 | Section 2.3 | dfdif3 3339 |
| [Pierik], p. 14 | Definition 3.1 | df-omni 7468 exmidomniim 7474 finomni 7473 |
| [Pierik], p. 15 | Section 3.1 | df-nninf 7453 |
| [Pradic2025], p. 2 | Section 1.1 | nnnninfen 16972 |
| [PradicBrown2022], p. 1 | Theorem 1 | exmidsbthr 16976 |
| [PradicBrown2022], p. 2 | Remark | exmidpw 7208 |
| [PradicBrown2022], p. 2 | Proposition 1.1 | exmidfodomrlemim 7546 |
| [PradicBrown2022], p. 2 | Proposition 1.2 | exmidfodomrlemr 7547 exmidfodomrlemrALT 7548 |
| [PradicBrown2022], p. 4 | Lemma 3.2 | fodjuomni 7482 |
| [PradicBrown2022], p. 5 | Lemma 3.4 | peano3nninf 16958 peano4nninf 16957 |
| [PradicBrown2022], p. 5 | Lemma 3.5 | nninfall 16960 |
| [PradicBrown2022], p. 5 | Theorem 3.6 | nninfsel 16968 |
| [PradicBrown2022], p. 5 | Corollary 3.7 | nninfomni 16970 |
| [PradicBrown2022], p. 5 | Definition 3.3 | nnsf 16956 |
| [Quine] p. 16 | Definition 2.1 | df-clab 2225 rabid 2727 |
| [Quine] p. 17 | Definition 2.1'' | dfsb7 2051 |
| [Quine] p. 18 | Definition 2.7 | df-cleq 2231 |
| [Quine] p. 19 | Definition 2.9 | df-v 2823 |
| [Quine] p. 34 | Theorem 5.1 | abeq2 2347 eqabb 2374 |
| [Quine] p. 35 | Theorem 5.2 | abid1 2372 abid2 2361 abid2f 2418 |
| [Quine] p. 40 | Theorem 6.1 | sb5 1942 |
| [Quine] p. 40 | Theorem 6.2 | sb56 1940 sb6 1941 |
| [Quine] p. 41 | Theorem 6.3 | df-clel 2234 |
| [Quine] p. 41 | Theorem 6.4 | eqid 2238 |
| [Quine] p. 41 | Theorem 6.5 | eqcom 2240 |
| [Quine] p. 42 | Theorem 6.6 | df-sbc 3052 |
| [Quine] p. 42 | Theorem 6.7 | dfsbcq 3053 dfsbcq2 3054 |
| [Quine] p. 43 | Theorem 6.8 | vex 2824 |
| [Quine] p. 43 | Theorem 6.9 | isset 2828 |
| [Quine] p. 44 | Theorem 7.3 | spcgf 2907 spcgv 2912 spcimgf 2905 |
| [Quine] p. 44 | Theorem 6.11 | spsbc 3063 spsbcd 3064 |
| [Quine] p. 44 | Theorem 6.12 | elex 2833 |
| [Quine] p. 44 | Theorem 6.13 | elab 2970 elabg 2972 elabgf 2968 |
| [Quine] p. 44 | Theorem 6.14 | noel 3525 |
| [Quine] p. 48 | Theorem 7.2 | snprc 3773 |
| [Quine] p. 48 | Definition 7.1 | df-pr 3715 df-sn 3714 |
| [Quine] p. 49 | Theorem 7.4 | snss 3848 snssg 3847 |
| [Quine] p. 49 | Theorem 7.5 | prss 3869 prssg 3870 |
| [Quine] p. 49 | Theorem 7.6 | prid1 3816 prid1g 3814 prid2 3817 prid2g 3815 snid 3739 snidg 3737 |
| [Quine] p. 51 | Theorem 7.12 | snexg 4319 snexprc 4321 |
| [Quine] p. 51 | Theorem 7.13 | prexg 4347 |
| [Quine] p. 53 | Theorem 8.2 | unisn 3949 unisng 3950 |
| [Quine] p. 53 | Theorem 8.3 | uniun 3952 |
| [Quine] p. 54 | Theorem 8.6 | elssuni 3961 |
| [Quine] p. 54 | Theorem 8.7 | uni0 3960 |
| [Quine] p. 56 | Theorem 8.17 | uniabio 5346 |
| [Quine] p. 56 | Definition 8.18 | dfiota2 5336 |
| [Quine] p. 57 | Theorem 8.19 | iotaval 5347 |
| [Quine] p. 57 | Theorem 8.22 | iotanul 5351 |
| [Quine] p. 58 | Theorem 8.23 | euiotaex 5352 |
| [Quine] p. 58 | Definition 9.1 | df-op 3717 |
| [Quine] p. 61 | Theorem 9.5 | opabid 4396 opabidw 4397 opelopab 4412 opelopaba 4406 opelopabaf 4414 opelopabf 4415 opelopabg 4408 opelopabga 4403 opelopabgf 4410 oprabid 6110 |
| [Quine] p. 64 | Definition 9.11 | df-xp 4778 |
| [Quine] p. 64 | Definition 9.12 | df-cnv 4780 |
| [Quine] p. 64 | Definition 9.15 | df-id 4436 |
| [Quine] p. 65 | Theorem 10.3 | fun0 5437 |
| [Quine] p. 65 | Theorem 10.4 | funi 5407 |
| [Quine] p. 65 | Theorem 10.5 | funsn 5427 funsng 5425 |
| [Quine] p. 65 | Definition 10.1 | df-fun 5377 |
| [Quine] p. 65 | Definition 10.2 | args 5154 dffv4g 5690 |
| [Quine] p. 68 | Definition 10.11 | df-fv 5383 fv2 5688 |
| [Quine] p. 124 | Theorem 17.3 | nn0opth2 11143 nn0opth2d 11142 nn0opthd 11141 |
| [Quine] p. 284 | Axiom 39(vi) | funimaex 5464 funimaexg 5463 |
| [Roman] p. 18 | Part Preliminaries | df-rng 14210 |
| [Roman] p. 19 | Part Preliminaries | df-ring 14279 |
| [Rudin] p. 164 | Equation 27 | efcan 12424 |
| [Rudin] p. 164 | Equation 30 | efzval 12431 |
| [Rudin] p. 167 | Equation 48 | absefi 12517 |
| [Sanford] p. 39 | Remark | ax-mp 5 |
| [Sanford] p. 39 | Rule 3 | mtpxor 1475 |
| [Sanford] p. 39 | Rule 4 | mptxor 1473 |
| [Sanford] p. 40 | Rule 1 | mptnan 1472 |
| [Schechter] p. 51 | Definition of antisymmetry | intasym 5170 |
| [Schechter] p. 51 | Definition of irreflexivity | intirr 5172 |
| [Schechter] p. 51 | Definition of symmetry | cnvsym 5169 |
| [Schechter] p. 51 | Definition of transitivity | cotr 5167 |
| [Schechter] p. 187 | Definition of "ring with unit" | isring 14281 |
| [Schechter] p. 428 | Definition 15.35 | bastop1 15110 |
| [Stoll] p. 13 | Definition of symmetric difference | symdif1 3496 |
| [Stoll] p. 16 | Exercise 4.4 | 0dif 3597 dif0 3596 |
| [Stoll] p. 16 | Exercise 4.8 | difdifdirss 3612 |
| [Stoll] p. 19 | Theorem 5.2(13) | undm 3489 |
| [Stoll] p. 19 | Theorem 5.2(13') | indmss 3490 |
| [Stoll] p. 20 | Remark | invdif 3473 |
| [Stoll] p. 25 | Definition of ordered triple | df-ot 3718 |
| [Stoll] p. 43 | Definition | uniiun 4064 |
| [Stoll] p. 44 | Definition | intiin 4065 |
| [Stoll] p. 45 | Definition | df-iin 4013 |
| [Stoll] p. 45 | Definition indexed union | df-iun 4012 |
| [Stoll] p. 176 | Theorem 3.4(27) | imandc 901 imanst 900 |
| [Stoll] p. 262 | Example 4.1 | symdif1 3496 |
| [Suppes] p. 22 | Theorem 2 | eq0 3540 |
| [Suppes] p. 22 | Theorem 4 | eqss 3263 eqssd 3265 eqssi 3264 |
| [Suppes] p. 23 | Theorem 5 | ss0 3563 ss0b 3562 |
| [Suppes] p. 23 | Theorem 6 | sstr 3256 |
| [Suppes] p. 25 | Theorem 12 | elin 3412 elun 3370 |
| [Suppes] p. 26 | Theorem 15 | inidm 3440 |
| [Suppes] p. 26 | Theorem 16 | in0 3557 |
| [Suppes] p. 27 | Theorem 23 | unidm 3372 |
| [Suppes] p. 27 | Theorem 24 | un0 3556 |
| [Suppes] p. 27 | Theorem 25 | ssun1 3392 |
| [Suppes] p. 27 | Theorem 26 | ssequn1 3399 |
| [Suppes] p. 27 | Theorem 27 | unss 3403 |
| [Suppes] p. 27 | Theorem 28 | indir 3480 |
| [Suppes] p. 27 | Theorem 29 | undir 3481 |
| [Suppes] p. 28 | Theorem 32 | difid 3594 difidALT 3595 |
| [Suppes] p. 29 | Theorem 33 | difin 3468 |
| [Suppes] p. 29 | Theorem 34 | indif 3474 |
| [Suppes] p. 29 | Theorem 35 | undif1ss 3602 |
| [Suppes] p. 29 | Theorem 36 | difun2 3607 |
| [Suppes] p. 29 | Theorem 37 | difin0 3601 |
| [Suppes] p. 29 | Theorem 38 | disjdif 3599 |
| [Suppes] p. 29 | Theorem 39 | difundi 3483 |
| [Suppes] p. 29 | Theorem 40 | difindiss 3485 |
| [Suppes] p. 30 | Theorem 41 | nalset 4261 |
| [Suppes] p. 39 | Theorem 61 | uniss 3954 |
| [Suppes] p. 39 | Theorem 65 | uniop 4394 |
| [Suppes] p. 41 | Theorem 70 | intsn 4003 |
| [Suppes] p. 42 | Theorem 71 | intpr 4000 intprg 4001 |
| [Suppes] p. 42 | Theorem 73 | op1stb 4622 op1stbg 4623 |
| [Suppes] p. 42 | Theorem 78 | intun 3999 |
| [Suppes] p. 44 | Definition 15(a) | dfiun2 4044 dfiun2g 4042 |
| [Suppes] p. 44 | Definition 15(b) | dfiin2 4045 |
| [Suppes] p. 47 | Theorem 86 | elpw 3694 elpw2 4291 elpw2g 4290 elpwg 3696 |
| [Suppes] p. 47 | Theorem 87 | pwid 3706 |
| [Suppes] p. 47 | Theorem 89 | pw0 3860 |
| [Suppes] p. 48 | Theorem 90 | pwpw0ss 3928 |
| [Suppes] p. 52 | Theorem 101 | xpss12 4880 |
| [Suppes] p. 52 | Theorem 102 | xpindi 4913 xpindir 4914 |
| [Suppes] p. 52 | Theorem 103 | xpundi 4829 xpundir 4830 |
| [Suppes] p. 54 | Theorem 105 | elirrv 4693 |
| [Suppes] p. 58 | Theorem 2 | relss 4860 |
| [Suppes] p. 59 | Theorem 4 | eldm 4976 eldm2 4977 eldm2g 4975 eldmg 4974 |
| [Suppes] p. 59 | Definition 3 | df-dm 4782 |
| [Suppes] p. 60 | Theorem 6 | dmin 4987 |
| [Suppes] p. 60 | Theorem 8 | rnun 5194 |
| [Suppes] p. 60 | Theorem 9 | rnin 5195 |
| [Suppes] p. 60 | Definition 4 | dfrn2 4966 |
| [Suppes] p. 61 | Theorem 11 | brcnv 4961 brcnvg 4959 |
| [Suppes] p. 62 | Equation 5 | elcnv 4955 elcnv2 4956 |
| [Suppes] p. 62 | Theorem 12 | relcnv 5163 |
| [Suppes] p. 62 | Theorem 15 | cnvin 5193 |
| [Suppes] p. 62 | Theorem 16 | cnvun 5191 |
| [Suppes] p. 63 | Theorem 20 | co02 5299 |
| [Suppes] p. 63 | Theorem 21 | dmcoss 5050 |
| [Suppes] p. 63 | Definition 7 | df-co 4781 |
| [Suppes] p. 64 | Theorem 26 | cnvco 4963 |
| [Suppes] p. 64 | Theorem 27 | coass 5304 |
| [Suppes] p. 65 | Theorem 31 | resundi 5074 |
| [Suppes] p. 65 | Theorem 34 | elima 5129 elima2 5130 elima3 5131 elimag 5128 |
| [Suppes] p. 65 | Theorem 35 | imaundi 5198 |
| [Suppes] p. 66 | Theorem 40 | dminss 5200 |
| [Suppes] p. 66 | Theorem 41 | imainss 5201 |
| [Suppes] p. 67 | Exercise 11 | cnvxp 5204 |
| [Suppes] p. 81 | Definition 34 | dfec2 6803 |
| [Suppes] p. 82 | Theorem 72 | elec 6841 elecg 6840 |
| [Suppes] p. 82 | Theorem 73 | erth 6846 erth2 6847 |
| [Suppes] p. 89 | Theorem 96 | map0b 6961 |
| [Suppes] p. 89 | Theorem 97 | map0 6964 map0g 6962 |
| [Suppes] p. 89 | Theorem 98 | mapsn 6965 mapsnd 6963 |
| [Suppes] p. 89 | Theorem 99 | mapss 6966 |
| [Suppes] p. 92 | Theorem 1 | enref 7044 enrefg 7043 |
| [Suppes] p. 92 | Theorem 2 | ensym 7061 ensymb 7060 ensymi 7062 |
| [Suppes] p. 92 | Theorem 3 | entr 7064 |
| [Suppes] p. 92 | Theorem 4 | unen 7098 |
| [Suppes] p. 94 | Theorem 15 | endom 7042 |
| [Suppes] p. 94 | Theorem 16 | ssdomg 7058 |
| [Suppes] p. 94 | Theorem 17 | domtr 7065 |
| [Suppes] p. 95 | Theorem 18 | isbth 7277 |
| [Suppes] p. 98 | Exercise 4 | fundmen 7087 fundmeng 7088 |
| [Suppes] p. 98 | Exercise 6 | xpdom3m 7125 |
| [Suppes] p. 130 | Definition 3 | df-tr 4228 |
| [Suppes] p. 132 | Theorem 9 | ssonuni 4633 |
| [Suppes] p. 134 | Definition 6 | df-suc 4514 |
| [Suppes] p. 136 | Theorem Schema 22 | findes 4748 finds 4745 finds1 4747 finds2 4746 |
| [Suppes] p. 162 | Definition 5 | df-ltnqqs 7713 df-ltpq 7706 |
| [Suppes] p. 228 | Theorem Schema 61 | onintss 4533 |
| [TakeutiZaring] p. 8 | Axiom 1 | ax-ext 2220 |
| [TakeutiZaring] p. 13 | Definition 4.5 | df-cleq 2231 |
| [TakeutiZaring] p. 13 | Proposition 4.6 | df-clel 2234 |
| [TakeutiZaring] p. 13 | Proposition 4.9 | cvjust 2233 |
| [TakeutiZaring] p. 13 | Proposition 4.7(3) | eqtr 2256 |
| [TakeutiZaring] p. 14 | Definition 4.16 | df-oprab 6082 |
| [TakeutiZaring] p. 14 | Proposition 4.14 | ru 3050 |
| [TakeutiZaring] p. 15 | Exercise 1 | elpr 3729 elpr2 3730 elprg 3728 |
| [TakeutiZaring] p. 15 | Exercise 2 | elsn 3724 elsn2 3742 elsn2g 3741 elsng 3723 velsn 3725 |
| [TakeutiZaring] p. 15 | Exercise 3 | elop 4369 |
| [TakeutiZaring] p. 15 | Exercise 4 | sneq 3719 sneqr 3883 |
| [TakeutiZaring] p. 15 | Definition 5.1 | dfpr2 3727 dfsn2 3722 |
| [TakeutiZaring] p. 16 | Axiom 3 | uniex 4581 |
| [TakeutiZaring] p. 16 | Exercise 6 | opth 4375 |
| [TakeutiZaring] p. 16 | Exercise 8 | rext 4353 |
| [TakeutiZaring] p. 16 | Corollary 5.8 | unex 4585 unexg 4587 |
| [TakeutiZaring] p. 16 | Definition 5.3 | dftp2 3757 |
| [TakeutiZaring] p. 16 | Definition 5.5 | df-uni 3934 |
| [TakeutiZaring] p. 16 | Definition 5.6 | df-in 3226 df-un 3224 |
| [TakeutiZaring] p. 16 | Proposition 5.7 | unipr 3947 uniprg 3948 |
| [TakeutiZaring] p. 17 | Axiom 4 | vpwex 4314 |
| [TakeutiZaring] p. 17 | Exercise 1 | eltp 3756 |
| [TakeutiZaring] p. 17 | Exercise 5 | elsuc 4549 elsucg 4547 sstr2 3255 |
| [TakeutiZaring] p. 17 | Exercise 6 | uncom 3373 |
| [TakeutiZaring] p. 17 | Exercise 7 | incom 3421 |
| [TakeutiZaring] p. 17 | Exercise 8 | unass 3386 |
| [TakeutiZaring] p. 17 | Exercise 9 | inass 3441 |
| [TakeutiZaring] p. 17 | Exercise 10 | indi 3478 |
| [TakeutiZaring] p. 17 | Exercise 11 | undi 3479 |
| [TakeutiZaring] p. 17 | Definition 5.9 | ssalel 3235 |
| [TakeutiZaring] p. 17 | Definition 5.10 | df-pw 3690 |
| [TakeutiZaring] p. 18 | Exercise 7 | unss2 3400 |
| [TakeutiZaring] p. 18 | Exercise 9 | df-ss 3233 dfss2 3237 sseqin2 3450 |
| [TakeutiZaring] p. 18 | Exercise 10 | ssid 3268 |
| [TakeutiZaring] p. 18 | Exercise 12 | inss1 3451 inss2 3452 |
| [TakeutiZaring] p. 18 | Exercise 13 | nssr 3308 |
| [TakeutiZaring] p. 18 | Exercise 15 | unieq 3942 |
| [TakeutiZaring] p. 18 | Exercise 18 | sspwb 4354 |
| [TakeutiZaring] p. 18 | Exercise 19 | pweqb 4361 |
| [TakeutiZaring] p. 20 | Definition | df-rab 2537 |
| [TakeutiZaring] p. 20 | Corollary 5.16 | 0ex 4258 |
| [TakeutiZaring] p. 20 | Definition 5.12 | df-dif 3222 |
| [TakeutiZaring] p. 20 | Definition 5.14 | dfnul2 3523 |
| [TakeutiZaring] p. 20 | Proposition 5.15 | difid 3594 difidALT 3595 |
| [TakeutiZaring] p. 20 | Proposition 5.17(1) | n0rf 3534 |
| [TakeutiZaring] p. 21 | Theorem 5.22 | setind 4684 |
| [TakeutiZaring] p. 21 | Definition 5.20 | df-v 2823 |
| [TakeutiZaring] p. 21 | Proposition 5.21 | vprc 4263 |
| [TakeutiZaring] p. 22 | Exercise 1 | 0ss 3561 |
| [TakeutiZaring] p. 22 | Exercise 3 | ssex 4268 ssexg 4270 |
| [TakeutiZaring] p. 22 | Exercise 4 | inex1 4265 |
| [TakeutiZaring] p. 22 | Exercise 5 | ruv 4695 |
| [TakeutiZaring] p. 22 | Exercise 6 | elirr 4686 |
| [TakeutiZaring] p. 22 | Exercise 7 | ssdif0im 3589 |
| [TakeutiZaring] p. 22 | Exercise 11 | difdif 3354 |
| [TakeutiZaring] p. 22 | Exercise 13 | undif3ss 3492 |
| [TakeutiZaring] p. 22 | Exercise 14 | difss 3355 |
| [TakeutiZaring] p. 22 | Exercise 15 | sscon 3363 |
| [TakeutiZaring] p. 22 | Definition 4.15(3) | df-ral 2533 |
| [TakeutiZaring] p. 22 | Definition 4.15(4) | df-rex 2534 |
| [TakeutiZaring] p. 23 | Proposition 6.2 | xpex 4889 xpexg 4887 xpexgALT 6359 |
| [TakeutiZaring] p. 23 | Definition 6.4(1) | df-rel 4779 |
| [TakeutiZaring] p. 23 | Definition 6.4(2) | fun2cnv 5443 |
| [TakeutiZaring] p. 24 | Definition 6.4(3) | f1cnvcnv 5607 fun11 5446 |
| [TakeutiZaring] p. 24 | Definition 6.4(4) | dffun4 5386 svrelfun 5444 |
| [TakeutiZaring] p. 24 | Definition 6.5(1) | dfdm3 4965 |
| [TakeutiZaring] p. 24 | Definition 6.5(2) | dfrn3 4967 |
| [TakeutiZaring] p. 24 | Definition 6.6(1) | df-res 4784 |
| [TakeutiZaring] p. 24 | Definition 6.6(2) | df-ima 4785 |
| [TakeutiZaring] p. 24 | Definition 6.6(3) | df-co 4781 |
| [TakeutiZaring] p. 25 | Exercise 2 | cnvcnvss 5240 dfrel2 5236 |
| [TakeutiZaring] p. 25 | Exercise 3 | xpss 4881 |
| [TakeutiZaring] p. 25 | Exercise 5 | relun 4892 |
| [TakeutiZaring] p. 25 | Exercise 6 | reluni 4898 |
| [TakeutiZaring] p. 25 | Exercise 9 | inxp 4912 |
| [TakeutiZaring] p. 25 | Exercise 12 | relres 5089 |
| [TakeutiZaring] p. 25 | Exercise 13 | opelres 5066 opelresg 5068 |
| [TakeutiZaring] p. 25 | Exercise 14 | dmres 5082 |
| [TakeutiZaring] p. 25 | Exercise 15 | resss 5085 |
| [TakeutiZaring] p. 25 | Exercise 17 | resabs1 5090 |
| [TakeutiZaring] p. 25 | Exercise 18 | funres 5416 |
| [TakeutiZaring] p. 25 | Exercise 24 | relco 5284 |
| [TakeutiZaring] p. 25 | Exercise 29 | funco 5415 |
| [TakeutiZaring] p. 25 | Exercise 30 | f1co 5608 |
| [TakeutiZaring] p. 26 | Definition 6.10 | eu2 2131 |
| [TakeutiZaring] p. 26 | Definition 6.11 | df-fv 5383 fv3 5716 |
| [TakeutiZaring] p. 26 | Corollary 6.8(1) | cnvex 5324 cnvexg 5323 |
| [TakeutiZaring] p. 26 | Corollary 6.8(2) | dmex 5047 dmexg 5044 |
| [TakeutiZaring] p. 26 | Corollary 6.8(3) | rnex 5048 rnexg 5045 |
| [TakeutiZaring] p. 26 | Corollary 6.9(2) | xpexcnvm 5140 |
| [TakeutiZaring] p. 27 | Corollary 6.13 | funfvex 5710 |
| [TakeutiZaring] p. 27 | Theorem 6.12(1) | tz6.12-1 5720 tz6.12 5721 tz6.12c 5723 |
| [TakeutiZaring] p. 27 | Theorem 6.12(2) | tz6.12-2 5684 |
| [TakeutiZaring] p. 27 | Definition 6.15(1) | df-fn 5378 |
| [TakeutiZaring] p. 27 | Definition 6.15(3) | df-f 5379 |
| [TakeutiZaring] p. 27 | Definition 6.15(4) | df-fo 5381 wfo 5373 |
| [TakeutiZaring] p. 27 | Definition 6.15(5) | df-f1 5380 wf1 5372 |
| [TakeutiZaring] p. 27 | Definition 6.15(6) | df-f1o 5382 wf1o 5374 |
| [TakeutiZaring] p. 28 | Exercise 4 | eqfnfv 5800 eqfnfv2 5801 eqfnfv2f 5804 |
| [TakeutiZaring] p. 28 | Exercise 5 | fvco 5772 |
| [TakeutiZaring] p. 28 | Theorem 6.16(1) | fnex 5931 fnexALT 6333 |
| [TakeutiZaring] p. 28 | Proposition 6.17 | resfunexg 5930 resfunexgALT 6330 |
| [TakeutiZaring] p. 29 | Exercise 9 | funimaex 5464 funimaexg 5463 |
| [TakeutiZaring] p. 29 | Definition 6.18 | df-br 4129 |
| [TakeutiZaring] p. 30 | Definition 6.21 | eliniseg 5155 iniseg 5157 |
| [TakeutiZaring] p. 30 | Definition 6.22 | df-eprel 4432 |
| [TakeutiZaring] p. 32 | Definition 6.28 | df-isom 5384 |
| [TakeutiZaring] p. 33 | Proposition 6.30(1) | isoid 6009 |
| [TakeutiZaring] p. 33 | Proposition 6.30(2) | isocnv 6010 |
| [TakeutiZaring] p. 33 | Proposition 6.30(3) | isotr 6015 |
| [TakeutiZaring] p. 33 | Proposition 6.31(2) | isoini 6017 |
| [TakeutiZaring] p. 34 | Proposition 6.33 | f1oiso 6025 |
| [TakeutiZaring] p. 35 | Notation | wtr 4227 |
| [TakeutiZaring] p. 35 | Theorem 7.2 | tz7.2 4497 |
| [TakeutiZaring] p. 35 | Definition 7.1 | dftr3 4231 |
| [TakeutiZaring] p. 36 | Proposition 7.4 | ordwe 4721 |
| [TakeutiZaring] p. 36 | Proposition 7.6 | ordelord 4524 |
| [TakeutiZaring] p. 37 | Proposition 7.9 | ordin 4528 |
| [TakeutiZaring] p. 38 | Corollary 7.15 | ordsson 4637 |
| [TakeutiZaring] p. 38 | Definition 7.11 | df-on 4511 |
| [TakeutiZaring] p. 38 | Proposition 7.12 | ordon 4631 |
| [TakeutiZaring] p. 38 | Proposition 7.13 | onprc 4697 |
| [TakeutiZaring] p. 39 | Theorem 7.17 | tfi 4727 |
| [TakeutiZaring] p. 40 | Exercise 7 | dftr2 4229 |
| [TakeutiZaring] p. 40 | Exercise 11 | unon 4656 |
| [TakeutiZaring] p. 40 | Proposition 7.19 | ssorduni 4632 |
| [TakeutiZaring] p. 40 | Proposition 7.20 | elssuni 3961 |
| [TakeutiZaring] p. 41 | Definition 7.22 | df-suc 4514 |
| [TakeutiZaring] p. 41 | Proposition 7.23 | sssucid 4558 sucidg 4559 |
| [TakeutiZaring] p. 41 | Proposition 7.24 | onsuc 4646 |
| [TakeutiZaring] p. 42 | Exercise 1 | df-ilim 4512 |
| [TakeutiZaring] p. 42 | Exercise 8 | onsucssi 4651 ordelsuc 4650 |
| [TakeutiZaring] p. 42 | Proposition 7.30(1) | peano1 4739 |
| [TakeutiZaring] p. 42 | Proposition 7.30(2) | peano2 4740 |
| [TakeutiZaring] p. 42 | Proposition 7.30(3) | peano3 4741 |
| [TakeutiZaring] p. 43 | Axiom 7 | omex 4738 |
| [TakeutiZaring] p. 43 | Theorem 7.32 | ordom 4752 |
| [TakeutiZaring] p. 43 | Corollary 7.31 | find 4744 |
| [TakeutiZaring] p. 43 | Proposition 7.30(4) | peano4 4742 |
| [TakeutiZaring] p. 43 | Proposition 7.30(5) | peano5 4743 |
| [TakeutiZaring] p. 44 | Exercise 2 | int0 3982 |
| [TakeutiZaring] p. 44 | Exercise 3 | trintssm 4243 |
| [TakeutiZaring] p. 44 | Exercise 4 | intss1 3983 |
| [TakeutiZaring] p. 44 | Exercise 6 | onintonm 4662 |
| [TakeutiZaring] p. 44 | Definition 7.35 | df-int 3969 |
| [TakeutiZaring] p. 47 | Lemma 1 | tfrlem1 6572 |
| [TakeutiZaring] p. 47 | Theorem 7.41(1) | tfri1 6629 tfri1d 6599 |
| [TakeutiZaring] p. 47 | Theorem 7.41(2) | tfri2 6630 tfri2d 6600 |
| [TakeutiZaring] p. 47 | Theorem 7.41(3) | tfri3 6631 |
| [TakeutiZaring] p. 50 | Exercise 3 | smoiso 6566 |
| [TakeutiZaring] p. 50 | Definition 7.46 | df-smo 6550 |
| [TakeutiZaring] p. 56 | Definition 8.1 | oasuc 6730 |
| [TakeutiZaring] p. 57 | Proposition 8.2 | oacl 6726 |
| [TakeutiZaring] p. 57 | Proposition 8.3 | oa0 6723 |
| [TakeutiZaring] p. 57 | Proposition 8.16 | omcl 6727 |
| [TakeutiZaring] p. 58 | Proposition 8.4 | nnaord 6775 nnaordi 6774 |
| [TakeutiZaring] p. 59 | Proposition 8.6 | iunss2 4055 uniss2 3964 |
| [TakeutiZaring] p. 59 | Proposition 8.7 | oawordriexmid 6736 |
| [TakeutiZaring] p. 59 | Proposition 8.9 | nnacl 6746 |
| [TakeutiZaring] p. 62 | Exercise 5 | oaword1 6737 |
| [TakeutiZaring] p. 62 | Definition 8.15 | om0 6724 omsuc 6738 |
| [TakeutiZaring] p. 63 | Proposition 8.17 | nnmcl 6747 |
| [TakeutiZaring] p. 63 | Proposition 8.19 | nnmord 6783 nnmordi 6782 |
| [TakeutiZaring] p. 67 | Definition 8.30 | oei0 6725 |
| [TakeutiZaring] p. 85 | Proposition 10.6(3) | cardonle 7525 |
| [TakeutiZaring] p. 88 | Exercise 1 | en0 7075 |
| [TakeutiZaring] p. 90 | Proposition 10.20 | nneneq 7151 |
| [TakeutiZaring] p. 90 | Corollary 10.21(1) | php5 7152 |
| [TakeutiZaring] p. 91 | Definition 10.29 | df-fin 7018 isfi 7040 |
| [TakeutiZaring] p. 92 | Proposition 10.33(2) | xpdom2 7122 |
| [TakeutiZaring] p. 95 | Definition 10.42 | df-map 6917 |
| [TakeutiZaring] p. 96 | Proposition 10.44 | pw2f1odc 7128 |
| [TakeutiZaring] p. 96 | Proposition 10.45 | mapxpen 7141 |
| [Tarski] p. 67 | Axiom B5 | ax-4 1563 |
| [Tarski] p. 68 | Lemma 6 | equid 1753 |
| [Tarski] p. 69 | Lemma 7 | equcomi 1756 |
| [Tarski] p. 70 | Lemma 14 | spim 1791 spime 1794 spimeh 1792 spimh 1790 |
| [Tarski] p. 70 | Lemma 16 | ax-11 1559 ax-11o 1876 ax11i 1766 |
| [Tarski] p. 70 | Lemmas 16 and 17 | sb6 1941 |
| [Tarski] p. 77 | Axiom B6 (p. 75) of system S2 | ax-17 1579 |
| [Tarski] p. 77 | Axiom B8 (p. 75) of system S2 | ax-13 2211 ax-14 2212 |
| [WhiteheadRussell] p. 96 | Axiom *1.3 | olc 723 |
| [WhiteheadRussell] p. 96 | Axiom *1.4 | pm1.4 739 |
| [WhiteheadRussell] p. 96 | Axiom *1.2 (Taut) | pm1.2 768 |
| [WhiteheadRussell] p. 96 | Axiom *1.5 (Assoc) | pm1.5 777 |
| [WhiteheadRussell] p. 97 | Axiom *1.6 (Sum) | orim2 801 |
| [WhiteheadRussell] p. 100 | Theorem *2.01 | pm2.01 625 |
| [WhiteheadRussell] p. 100 | Theorem *2.02 | ax-1 6 |
| [WhiteheadRussell] p. 100 | Theorem *2.03 | con2 652 |
| [WhiteheadRussell] p. 100 | Theorem *2.04 | pm2.04 82 |
| [WhiteheadRussell] p. 100 | Theorem *2.05 | imim2 55 |
| [WhiteheadRussell] p. 100 | Theorem *2.06 | imim1 76 |
| [WhiteheadRussell] p. 101 | Theorem *2.1 | pm2.1dc 849 |
| [WhiteheadRussell] p. 101 | Theorem *2.06 | barbara 2185 syl 14 |
| [WhiteheadRussell] p. 101 | Theorem *2.07 | pm2.07 749 |
| [WhiteheadRussell] p. 101 | Theorem *2.08 | id 19 idALT 20 |
| [WhiteheadRussell] p. 101 | Theorem *2.11 | exmiddc 848 |
| [WhiteheadRussell] p. 101 | Theorem *2.12 | notnot 638 |
| [WhiteheadRussell] p. 101 | Theorem *2.13 | pm2.13dc 897 |
| [WhiteheadRussell] p. 102 | Theorem *2.14 | notnotrdc 855 |
| [WhiteheadRussell] p. 102 | Theorem *2.15 | con1dc 868 |
| [WhiteheadRussell] p. 103 | Theorem *2.16 | con3 651 |
| [WhiteheadRussell] p. 103 | Theorem *2.17 | condc 865 |
| [WhiteheadRussell] p. 103 | Theorem *2.18 | pm2.18dc 867 |
| [WhiteheadRussell] p. 104 | Theorem *2.2 | orc 724 |
| [WhiteheadRussell] p. 104 | Theorem *2.3 | pm2.3 787 |
| [WhiteheadRussell] p. 104 | Theorem *2.21 | pm2.21 626 |
| [WhiteheadRussell] p. 104 | Theorem *2.24 | pm2.24 630 |
| [WhiteheadRussell] p. 104 | Theorem *2.25 | pm2.25dc 905 |
| [WhiteheadRussell] p. 104 | Theorem *2.26 | pm2.26dc 919 |
| [WhiteheadRussell] p. 104 | Theorem *2.27 | pm2.27 40 |
| [WhiteheadRussell] p. 104 | Theorem *2.31 | pm2.31 780 |
| [WhiteheadRussell] p. 105 | Theorem *2.32 | pm2.32 781 |
| [WhiteheadRussell] p. 105 | Theorem *2.36 | pm2.36 816 |
| [WhiteheadRussell] p. 105 | Theorem *2.37 | pm2.37 817 |
| [WhiteheadRussell] p. 105 | Theorem *2.38 | pm2.38 815 |
| [WhiteheadRussell] p. 105 | Definition *2.33 | df-3or 1010 |
| [WhiteheadRussell] p. 106 | Theorem *2.4 | pm2.4 790 |
| [WhiteheadRussell] p. 106 | Theorem *2.41 | pm2.41 788 |
| [WhiteheadRussell] p. 106 | Theorem *2.42 | pm2.42 789 |
| [WhiteheadRussell] p. 106 | Theorem *2.43 | pm2.43 53 |
| [WhiteheadRussell] p. 106 | Theorem *2.45 | pm2.45 750 |
| [WhiteheadRussell] p. 106 | Theorem *2.46 | pm2.46 751 |
| [WhiteheadRussell] p. 107 | Theorem *2.5 | pm2.5dc 879 pm2.5gdc 878 |
| [WhiteheadRussell] p. 107 | Theorem *2.6 | pm2.6dc 874 |
| [WhiteheadRussell] p. 107 | Theorem *2.47 | pm2.47 752 |
| [WhiteheadRussell] p. 107 | Theorem *2.48 | pm2.48 753 |
| [WhiteheadRussell] p. 107 | Theorem *2.49 | pm2.49 754 |
| [WhiteheadRussell] p. 107 | Theorem *2.51 | pm2.51 665 |
| [WhiteheadRussell] p. 107 | Theorem *2.52 | pm2.52 666 |
| [WhiteheadRussell] p. 107 | Theorem *2.53 | pm2.53 734 |
| [WhiteheadRussell] p. 107 | Theorem *2.54 | pm2.54dc 903 |
| [WhiteheadRussell] p. 107 | Theorem *2.55 | orel1 737 |
| [WhiteheadRussell] p. 107 | Theorem *2.56 | orel2 738 |
| [WhiteheadRussell] p. 107 | Theorem *2.61 | pm2.61dc 877 |
| [WhiteheadRussell] p. 107 | Theorem *2.62 | pm2.62 760 |
| [WhiteheadRussell] p. 107 | Theorem *2.63 | pm2.63 812 |
| [WhiteheadRussell] p. 107 | Theorem *2.64 | pm2.64 813 |
| [WhiteheadRussell] p. 107 | Theorem *2.65 | pm2.65 669 |
| [WhiteheadRussell] p. 107 | Theorem *2.67 | pm2.67-2 725 pm2.67 755 |
| [WhiteheadRussell] p. 107 | Theorem *2.521 | pm2.521dc 881 pm2.521gdc 880 |
| [WhiteheadRussell] p. 107 | Theorem *2.621 | pm2.621 759 |
| [WhiteheadRussell] p. 108 | Theorem *2.8 | pm2.8 822 |
| [WhiteheadRussell] p. 108 | Theorem *2.68 | pm2.68dc 906 |
| [WhiteheadRussell] p. 108 | Theorem *2.69 | looinvdc 927 |
| [WhiteheadRussell] p. 108 | Theorem *2.73 | pm2.73 818 |
| [WhiteheadRussell] p. 108 | Theorem *2.74 | pm2.74 819 |
| [WhiteheadRussell] p. 108 | Theorem *2.75 | pm2.75 821 |
| [WhiteheadRussell] p. 108 | Theorem *2.76 | pm2.76 820 |
| [WhiteheadRussell] p. 108 | Theorem *2.77 | ax-2 7 |
| [WhiteheadRussell] p. 108 | Theorem *2.81 | pm2.81 823 |
| [WhiteheadRussell] p. 108 | Theorem *2.82 | pm2.82 824 |
| [WhiteheadRussell] p. 108 | Theorem *2.83 | pm2.83 77 |
| [WhiteheadRussell] p. 108 | Theorem *2.85 | pm2.85dc 917 |
| [WhiteheadRussell] p. 108 | Theorem *2.86 | pm2.86 101 |
| [WhiteheadRussell] p. 111 | Theorem *3.1 | pm3.1 766 |
| [WhiteheadRussell] p. 111 | Theorem *3.2 | pm3.2 139 |
| [WhiteheadRussell] p. 111 | Theorem *3.11 | pm3.11dc 970 |
| [WhiteheadRussell] p. 111 | Theorem *3.12 | pm3.12dc 971 |
| [WhiteheadRussell] p. 111 | Theorem *3.13 | pm3.13dc 972 |
| [WhiteheadRussell] p. 111 | Theorem *3.14 | pm3.14 765 |
| [WhiteheadRussell] p. 111 | Theorem *3.21 | pm3.21 264 |
| [WhiteheadRussell] p. 111 | Theorem *3.22 | pm3.22 265 |
| [WhiteheadRussell] p. 111 | Theorem *3.24 | pm3.24 705 |
| [WhiteheadRussell] p. 112 | Theorem *3.35 | pm3.35 347 |
| [WhiteheadRussell] p. 112 | Theorem *3.3 (Exp) | pm3.3 261 |
| [WhiteheadRussell] p. 112 | Theorem *3.31 (Imp) | pm3.31 262 |
| [WhiteheadRussell] p. 112 | Theorem *3.26 (Simp) | simpl 109 simplimdc 872 |
| [WhiteheadRussell] p. 112 | Theorem *3.27 (Simp) | simpr 110 simprimdc 871 |
| [WhiteheadRussell] p. 112 | Theorem *3.33 (Syll) | pm3.33 345 |
| [WhiteheadRussell] p. 112 | Theorem *3.34 (Syll) | pm3.34 346 |
| [WhiteheadRussell] p. 112 | Theorem *3.37 (Transp) | pm3.37 700 |
| [WhiteheadRussell] p. 113 | Fact) | pm3.45 605 |
| [WhiteheadRussell] p. 113 | Theorem *3.4 | pm3.4 333 |
| [WhiteheadRussell] p. 113 | Theorem *3.41 | pm3.41 331 |
| [WhiteheadRussell] p. 113 | Theorem *3.42 | pm3.42 332 |
| [WhiteheadRussell] p. 113 | Theorem *3.44 | jao 767 pm3.44 727 |
| [WhiteheadRussell] p. 113 | Theorem *3.47 | anim12 344 |
| [WhiteheadRussell] p. 113 | Theorem *3.43 (Comp) | pm3.43 610 |
| [WhiteheadRussell] p. 114 | Theorem *3.48 | pm3.48 797 |
| [WhiteheadRussell] p. 116 | Theorem *4.1 | con34bdc 883 |
| [WhiteheadRussell] p. 117 | Theorem *4.2 | biid 171 |
| [WhiteheadRussell] p. 117 | Theorem *4.13 | notnotbdc 884 |
| [WhiteheadRussell] p. 117 | Theorem *4.14 | pm4.14dc 902 |
| [WhiteheadRussell] p. 117 | Theorem *4.15 | pm4.15 706 |
| [WhiteheadRussell] p. 117 | Theorem *4.21 | bicom 140 |
| [WhiteheadRussell] p. 117 | Theorem *4.22 | biantr 965 bitr 476 |
| [WhiteheadRussell] p. 117 | Theorem *4.24 | pm4.24 399 |
| [WhiteheadRussell] p. 117 | Theorem *4.25 | oridm 769 pm4.25 770 |
| [WhiteheadRussell] p. 118 | Theorem *4.3 | ancom 266 |
| [WhiteheadRussell] p. 118 | Theorem *4.4 | andi 830 |
| [WhiteheadRussell] p. 118 | Theorem *4.31 | orcom 740 |
| [WhiteheadRussell] p. 118 | Theorem *4.32 | anass 405 |
| [WhiteheadRussell] p. 118 | Theorem *4.33 | orass 779 |
| [WhiteheadRussell] p. 118 | Theorem *4.36 | anbi1 470 |
| [WhiteheadRussell] p. 118 | Theorem *4.37 | orbi1 804 |
| [WhiteheadRussell] p. 118 | Theorem *4.38 | pm4.38 613 |
| [WhiteheadRussell] p. 118 | Theorem *4.39 | pm4.39 834 |
| [WhiteheadRussell] p. 118 | Definition *4.34 | df-3an 1011 |
| [WhiteheadRussell] p. 119 | Theorem *4.41 | ordi 828 |
| [WhiteheadRussell] p. 119 | Theorem *4.42 | pm4.42r 984 |
| [WhiteheadRussell] p. 119 | Theorem *4.43 | pm4.43 962 |
| [WhiteheadRussell] p. 119 | Theorem *4.44 | pm4.44 791 |
| [WhiteheadRussell] p. 119 | Theorem *4.45 | orabs 826 pm4.45 796 pm4.45im 334 |
| [WhiteheadRussell] p. 119 | Theorem *10.22 | 19.26 1534 |
| [WhiteheadRussell] p. 120 | Theorem *4.5 | anordc 969 |
| [WhiteheadRussell] p. 120 | Theorem *4.6 | imordc 909 imorr 733 |
| [WhiteheadRussell] p. 120 | Theorem *4.7 | anclb 319 |
| [WhiteheadRussell] p. 120 | Theorem *4.51 | ianordc 911 |
| [WhiteheadRussell] p. 120 | Theorem *4.52 | pm4.52im 762 |
| [WhiteheadRussell] p. 120 | Theorem *4.53 | pm4.53r 763 |
| [WhiteheadRussell] p. 120 | Theorem *4.54 | pm4.54dc 914 |
| [WhiteheadRussell] p. 120 | Theorem *4.55 | pm4.55dc 951 |
| [WhiteheadRussell] p. 120 | Theorem *4.56 | ioran 764 pm4.56 792 |
| [WhiteheadRussell] p. 120 | Theorem *4.57 | orandc 952 oranim 793 |
| [WhiteheadRussell] p. 120 | Theorem *4.61 | annimim 697 |
| [WhiteheadRussell] p. 120 | Theorem *4.62 | pm4.62dc 910 |
| [WhiteheadRussell] p. 120 | Theorem *4.63 | pm4.63dc 898 |
| [WhiteheadRussell] p. 120 | Theorem *4.64 | pm4.64dc 912 |
| [WhiteheadRussell] p. 120 | Theorem *4.65 | pm4.65r 698 |
| [WhiteheadRussell] p. 120 | Theorem *4.66 | pm4.66dc 913 |
| [WhiteheadRussell] p. 120 | Theorem *4.67 | pm4.67dc 899 |
| [WhiteheadRussell] p. 120 | Theorem *4.71 | pm4.71 393 pm4.71d 397 pm4.71i 395 pm4.71r 394 pm4.71rd 398 pm4.71ri 396 |
| [WhiteheadRussell] p. 121 | Theorem *4.72 | pm4.72 839 |
| [WhiteheadRussell] p. 121 | Theorem *4.73 | iba 300 |
| [WhiteheadRussell] p. 121 | Theorem *4.74 | biorf 756 |
| [WhiteheadRussell] p. 121 | Theorem *4.76 | jcab 611 pm4.76 612 |
| [WhiteheadRussell] p. 121 | Theorem *4.77 | jaob 722 pm4.77 811 |
| [WhiteheadRussell] p. 121 | Theorem *4.78 | pm4.78i 794 |
| [WhiteheadRussell] p. 121 | Theorem *4.79 | pm4.79dc 915 |
| [WhiteheadRussell] p. 122 | Theorem *4.8 | pm4.8 719 |
| [WhiteheadRussell] p. 122 | Theorem *4.81 | pm4.81dc 920 |
| [WhiteheadRussell] p. 122 | Theorem *4.82 | pm4.82 963 |
| [WhiteheadRussell] p. 122 | Theorem *4.83 | pm4.83dc 964 |
| [WhiteheadRussell] p. 122 | Theorem *4.84 | imbi1 236 |
| [WhiteheadRussell] p. 122 | Theorem *4.85 | imbi2 237 |
| [WhiteheadRussell] p. 122 | Theorem *4.86 | bibi1 240 |
| [WhiteheadRussell] p. 122 | Theorem *4.87 | bi2.04 248 impexp 263 pm4.87 563 |
| [WhiteheadRussell] p. 123 | Theorem *5.1 | pm5.1 609 |
| [WhiteheadRussell] p. 123 | Theorem *5.11 | pm5.11dc 921 |
| [WhiteheadRussell] p. 123 | Theorem *5.12 | pm5.12dc 922 |
| [WhiteheadRussell] p. 123 | Theorem *5.13 | pm5.13dc 924 |
| [WhiteheadRussell] p. 123 | Theorem *5.14 | pm5.14dc 923 |
| [WhiteheadRussell] p. 124 | Theorem *5.15 | pm5.15dc 1438 |
| [WhiteheadRussell] p. 124 | Theorem *5.16 | pm5.16 840 |
| [WhiteheadRussell] p. 124 | Theorem *5.17 | pm5.17dc 916 |
| [WhiteheadRussell] p. 124 | Theorem *5.18 | nbbndc 1443 pm5.18dc 895 |
| [WhiteheadRussell] p. 124 | Theorem *5.19 | pm5.19 718 |
| [WhiteheadRussell] p. 124 | Theorem *5.21 | pm5.21 707 |
| [WhiteheadRussell] p. 124 | Theorem *5.22 | xordc 1441 |
| [WhiteheadRussell] p. 124 | Theorem *5.23 | dfbi3dc 1446 |
| [WhiteheadRussell] p. 124 | Theorem *5.24 | pm5.24dc 1447 |
| [WhiteheadRussell] p. 124 | Theorem *5.25 | dfor2dc 907 |
| [WhiteheadRussell] p. 125 | Theorem *5.3 | pm5.3 479 |
| [WhiteheadRussell] p. 125 | Theorem *5.4 | pm5.4 249 |
| [WhiteheadRussell] p. 125 | Theorem *5.5 | pm5.5 242 |
| [WhiteheadRussell] p. 125 | Theorem *5.6 | pm5.6dc 938 pm5.6r 939 |
| [WhiteheadRussell] p. 125 | Theorem *5.7 | pm5.7dc 967 |
| [WhiteheadRussell] p. 125 | Theorem *5.31 | pm5.31 348 |
| [WhiteheadRussell] p. 125 | Theorem *5.32 | pm5.32 457 |
| [WhiteheadRussell] p. 125 | Theorem *5.33 | pm5.33 617 |
| [WhiteheadRussell] p. 125 | Theorem *5.35 | pm5.35 929 |
| [WhiteheadRussell] p. 125 | Theorem *5.36 | pm5.36 618 |
| [WhiteheadRussell] p. 125 | Theorem *5.41 | imdi 250 pm5.41 251 |
| [WhiteheadRussell] p. 125 | Theorem *5.42 | pm5.42 320 |
| [WhiteheadRussell] p. 125 | Theorem *5.44 | pm5.44 937 |
| [WhiteheadRussell] p. 125 | Theorem *5.53 | pm5.53 814 |
| [WhiteheadRussell] p. 125 | Theorem *5.54 | pm5.54dc 930 |
| [WhiteheadRussell] p. 125 | Theorem *5.55 | pm5.55dc 925 |
| [WhiteheadRussell] p. 125 | Theorem *5.61 | pm5.61 806 |
| [WhiteheadRussell] p. 125 | Theorem *5.62 | pm5.62dc 958 |
| [WhiteheadRussell] p. 125 | Theorem *5.63 | pm5.63dc 959 |
| [WhiteheadRussell] p. 125 | Theorem *5.71 | pm5.71dc 974 |
| [WhiteheadRussell] p. 125 | Theorem *5.501 | pm5.501 244 |
| [WhiteheadRussell] p. 126 | Theorem *5.74 | pm5.74 179 |
| [WhiteheadRussell] p. 126 | Theorem *5.75 | pm5.75 975 |
| [WhiteheadRussell] p. 150 | Theorem *10.3 | alsyl 1688 |
| [WhiteheadRussell] p. 160 | Theorem *11.21 | alrot3 1538 |
| [WhiteheadRussell] p. 163 | Theorem *11.42 | 19.40-2 1685 |
| [WhiteheadRussell] p. 164 | Theorem *11.53 | pm11.53 1951 |
| [WhiteheadRussell] p. 175 | Definition *14.02 | df-eu 2089 |
| [WhiteheadRussell] p. 178 | Theorem *13.18 | pm13.18 2501 |
| [WhiteheadRussell] p. 178 | Theorem *13.181 | pm13.181 2502 |
| [WhiteheadRussell] p. 178 | Theorem *13.183 | pm13.183 2964 |
| [WhiteheadRussell] p. 185 | Theorem *14.121 | sbeqalb 3108 |
| [WhiteheadRussell] p. 190 | Theorem *14.22 | iota4 5355 |
| [WhiteheadRussell] p. 191 | Theorem *14.23 | iota4an 5356 |
| [WhiteheadRussell] p. 192 | Theorem *14.26 | eupick 2166 eupickbi 2169 |
| [WhiteheadRussell] p. 235 | Definition *30.01 | df-fv 5383 |
| [WhiteheadRussell] p. 360 | Theorem *54.43 | pm54.43 7529 |
| [vandenDries] p. 43 | Theorem 62 | pellexlem1 16008 |
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