Colors of
variables: wff set class |
Syntax hints: wi 4
wa 104
wcel 2146
cfv 5208
(class class class)co 5865 cc 7784 cr 7785 cmul 7791 crp 9622 ce 11617 clog 13770 ccxp 13771 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709
ax-5 1445 ax-7 1446 ax-gen 1447 ax-ie1 1491 ax-ie2 1492 ax-8 1502 ax-10 1503 ax-11 1504 ax-i12 1505 ax-bndl 1507 ax-4 1508 ax-17 1524 ax-i9 1528 ax-ial 1532 ax-i5r 1533 ax-13 2148 ax-14 2149 ax-ext 2157 ax-coll 4113 ax-sep 4116 ax-nul 4124 ax-pow 4169 ax-pr 4203 ax-un 4427 ax-setind 4530 ax-iinf 4581 ax-cnex 7877 ax-resscn 7878 ax-1cn 7879 ax-1re 7880 ax-icn 7881 ax-addcl 7882 ax-addrcl 7883 ax-mulcl 7884 ax-mulrcl 7885 ax-addcom 7886 ax-mulcom 7887 ax-addass 7888 ax-mulass 7889 ax-distr 7890 ax-i2m1 7891 ax-0lt1 7892 ax-1rid 7893 ax-0id 7894 ax-rnegex 7895 ax-precex 7896 ax-cnre 7897 ax-pre-ltirr 7898 ax-pre-ltwlin 7899 ax-pre-lttrn 7900 ax-pre-apti 7901 ax-pre-ltadd 7902 ax-pre-mulgt0 7903 ax-pre-mulext 7904 ax-arch 7905 ax-caucvg 7906 ax-pre-suploc 7907 ax-addf 7908 ax-mulf 7909 |
This theorem depends on definitions:
df-bi 117 df-stab 831 df-dc 835
df-3or 979 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1459 df-sb 1761 df-eu 2027 df-mo 2028 df-clab 2162 df-cleq 2168 df-clel 2171 df-nfc 2306 df-ne 2346 df-nel 2441 df-ral 2458 df-rex 2459 df-reu 2460 df-rmo 2461 df-rab 2462 df-v 2737 df-sbc 2961 df-csb 3056 df-dif 3129 df-un 3131 df-in 3133 df-ss 3140 df-nul 3421 df-if 3533 df-pw 3574 df-sn 3595 df-pr 3596 df-op 3598 df-uni 3806 df-int 3841 df-iun 3884 df-disj 3976 df-br 3999 df-opab 4060 df-mpt 4061 df-tr 4097 df-id 4287 df-po 4290 df-iso 4291 df-iord 4360 df-on 4362 df-ilim 4363 df-suc 4365 df-iom 4584 df-xp 4626 df-rel 4627 df-cnv 4628 df-co 4629 df-dm 4630 df-rn 4631 df-res 4632 df-ima 4633 df-iota 5170 df-fun 5210 df-fn 5211 df-f 5212 df-f1 5213 df-fo 5214 df-f1o 5215 df-fv 5216 df-isom 5217 df-riota 5821 df-ov 5868 df-oprab 5869 df-mpo 5870 df-of 6073 df-1st 6131 df-2nd 6132 df-recs 6296 df-irdg 6361 df-frec 6382 df-1o 6407 df-oadd 6411 df-er 6525 df-map 6640 df-pm 6641 df-en 6731 df-dom 6732 df-fin 6733 df-sup 6973 df-inf 6974 df-pnf 7968 df-mnf 7969 df-xr 7970 df-ltxr 7971 df-le 7972 df-sub 8104 df-neg 8105 df-reap 8506 df-ap 8513 df-div 8602 df-inn 8891 df-2 8949 df-3 8950
df-4 8951 df-n0 9148 df-z 9225 df-uz 9500 df-q 9591 df-rp 9623 df-xneg 9741 df-xadd 9742 df-ioo 9861 df-ico 9863 df-icc 9864 df-fz 9978 df-fzo 10111 df-seqfrec 10414 df-exp 10488 df-fac 10672 df-bc 10694 df-ihash 10722 df-shft 10791 df-cj 10818 df-re 10819 df-im 10820 df-rsqrt 10974 df-abs 10975 df-clim 11254 df-sumdc 11329 df-ef 11623 df-e 11624
df-rest 12611 df-topgen 12630 df-psmet 12980 df-xmet 12981 df-met 12982 df-bl 12983 df-mopn 12984 df-top 12989 df-topon 13002 df-bases 13034 df-ntr 13089 df-cn 13181 df-cnp 13182 df-tx 13246 df-cncf 13551 df-limced 13618 df-dvap 13619 df-relog 13772 df-rpcxp 13773 |
This theorem is referenced by: rpcxpneg
13821 rpcxpsub
13822 cxprec
13824 rpdivcxp
13825 rpcncxpcld
13840 |