| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 ∧ wa 395
∈ wcel 2105 (class class class)co 7412
Sℋ csh 30614
Cℋ cch 30615
∨ℋ chj 30619 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912
ax-6 1970 ax-7 2010 ax-8 2107
ax-9 2115 ax-10 2136 ax-11 2153 ax-12 2170 ax-ext 2702 ax-rep 5285 ax-sep 5299 ax-nul 5306 ax-pow 5363 ax-pr 5427 ax-un 7729 ax-inf2 9642 ax-cnex 11172 ax-resscn 11173 ax-1cn 11174 ax-icn 11175 ax-addcl 11176 ax-addrcl 11177 ax-mulcl 11178 ax-mulrcl 11179 ax-mulcom 11180 ax-addass 11181 ax-mulass 11182 ax-distr 11183 ax-i2m1 11184 ax-1ne0 11185 ax-1rid 11186 ax-rnegex 11187 ax-rrecex 11188 ax-cnre 11189 ax-pre-lttri 11190 ax-pre-lttrn 11191 ax-pre-ltadd 11192 ax-pre-mulgt0 11193 ax-pre-sup 11194 ax-addf 11195 ax-mulf 11196 ax-hilex 30685 ax-hfvadd 30686 ax-hvcom 30687 ax-hvass 30688 ax-hv0cl 30689 ax-hvaddid 30690 ax-hfvmul 30691 ax-hvmulid 30692 ax-hvmulass 30693 ax-hvdistr1 30694 ax-hvdistr2 30695 ax-hvmul0 30696 ax-hfi 30765 ax-his1 30768 ax-his2 30769 ax-his3 30770 ax-his4 30771 ax-hcompl 30888 |
| This theorem depends on definitions:
df-bi 206 df-an 396
df-or 845 df-3or 1087 df-3an 1088 df-tru 1543 df-fal 1553 df-ex 1781 df-nf 1785 df-sb 2067 df-mo 2533 df-eu 2562 df-clab 2709 df-cleq 2723 df-clel 2809 df-nfc 2884 df-ne 2940 df-nel 3046 df-ral 3061 df-rex 3070 df-rmo 3375 df-reu 3376 df-rab 3432 df-v 3475 df-sbc 3778 df-csb 3894 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-pss 3967 df-nul 4323 df-if 4529 df-pw 4604 df-sn 4629 df-pr 4631 df-tp 4633 df-op 4635 df-uni 4909 df-int 4951 df-iun 4999 df-iin 5000 df-br 5149 df-opab 5211 df-mpt 5232 df-tr 5266 df-id 5574 df-eprel 5580 df-po 5588 df-so 5589 df-fr 5631 df-se 5632 df-we 5633 df-xp 5682 df-rel 5683 df-cnv 5684 df-co 5685 df-dm 5686 df-rn 5687 df-res 5688 df-ima 5689 df-pred 6300 df-ord 6367 df-on 6368 df-lim 6369 df-suc 6370 df-iota 6495 df-fun 6545 df-fn 6546 df-f 6547 df-f1 6548 df-fo 6549 df-f1o 6550 df-fv 6551 df-isom 6552 df-riota 7368 df-ov 7415 df-oprab 7416 df-mpo 7417 df-of 7674 df-om 7860 df-1st 7979 df-2nd 7980 df-supp 8152 df-frecs 8272 df-wrecs 8303 df-recs 8377 df-rdg 8416 df-1o 8472 df-2o 8473 df-er 8709 df-map 8828 df-pm 8829 df-ixp 8898 df-en 8946 df-dom 8947 df-sdom 8948 df-fin 8949 df-fsupp 9368 df-fi 9412 df-sup 9443 df-inf 9444 df-oi 9511 df-card 9940 df-pnf 11257 df-mnf 11258 df-xr 11259 df-ltxr 11260 df-le 11261 df-sub 11453 df-neg 11454 df-div 11879 df-nn 12220 df-2 12282
df-3 12283 df-4 12284
df-5 12285 df-6 12286
df-7 12287 df-8 12288
df-9 12289 df-n0 12480 df-z 12566
df-dec 12685 df-uz 12830 df-q 12940
df-rp 12982 df-xneg 13099 df-xadd 13100 df-xmul 13101 df-ioo 13335 df-icc 13338 df-fz 13492 df-fzo 13635 df-seq 13974 df-exp 14035 df-hash 14298 df-cj 15053 df-re 15054 df-im 15055 df-sqrt 15189 df-abs 15190 df-clim 15439 df-sum 15640 df-struct 17087 df-sets 17104 df-slot 17122 df-ndx 17134 df-base 17152 df-ress 17181 df-plusg 17217 df-mulr 17218 df-starv 17219 df-sca 17220 df-vsca 17221 df-ip 17222 df-tset 17223 df-ple 17224 df-ds 17226 df-unif 17227 df-hom 17228 df-cco 17229 df-rest 17375 df-topn 17376 df-0g 17394 df-gsum 17395 df-topgen 17396 df-pt 17397 df-prds 17400 df-xrs 17455 df-qtop 17460 df-imas 17461 df-xps 17463 df-mre 17537 df-mrc 17538 df-acs 17540 df-mgm 18571 df-sgrp 18650 df-mnd 18666 df-submnd 18712 df-mulg 18994 df-cntz 19229 df-cmn 19698 df-psmet 21225 df-xmet 21226 df-met 21227 df-bl 21228 df-mopn 21229 df-cnfld 21234 df-top 22716 df-topon 22733 df-topsp 22755 df-bases 22769 df-cn 23051 df-cnp 23052 df-lm 23053 df-haus 23139 df-tx 23386 df-hmeo 23579 df-xms 24146 df-ms 24147 df-tms 24148 df-cau 25104 df-grpo 30179 df-gid 30180 df-ginv 30181 df-gdiv 30182 df-ablo 30231 df-vc 30245 df-nv 30278 df-va 30281 df-ba 30282 df-sm 30283 df-0v 30284 df-vs 30285 df-nmcv 30286 df-ims 30287 df-dip 30387 df-hnorm 30654 df-hvsub 30657 df-hlim 30658 df-hcau 30659 df-sh 30893 df-ch 30907 df-oc 30938 df-chj 30996 |
| This theorem is referenced by: chj4
31221 cm0
31295 pjoml5
31299 fh1
31304 fh2
31305 cm2j
31306 spansnscl
31334 hstle
31916 strlem3a
31938 hstrlem3a
31946 spansncv2
31979 mdbr2
31982 dmdmd
31986 dmdbr3
31991 dmdbr4
31992 dmdbr5
31994 mdsl1i
32007 mdsl2i
32008 mdslmd1i
32015 mdexchi
32021 cvdmd
32023 chcv1
32041 cvati
32052 cvexchlem
32054 atcv0eq
32065 atexch
32067 atomli
32068 atcvatlem
32071 atcvat2i
32073 chirredlem3
32078 atcvat3i
32082 atcvat4i
32083 mdsymlem1
32089 mdsymlem3
32091 mdsymlem5
32093 mdsymlem6
32094 dmdbr5ati
32108 |
