| Colors of
variables: wff set class |
Syntax hints:  wi 4
![/\](wedge.gif "/\") wa 104
 wb 105  wceq 1353  wcel 2148 class class class wbr 4002
(class class class)co 5871  cc 7805  cc0 7807  c1 7808  cmul 7812 # cap 8533
 cdiv 8624 |
| 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 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4120 ax-pow 4173 ax-pr 4208 ax-un 4432 ax-setind 4535 ax-cnex 7898 ax-resscn 7899 ax-1cn 7900 ax-1re 7901 ax-icn 7902 ax-addcl 7903 ax-addrcl 7904 ax-mulcl 7905 ax-mulrcl 7906 ax-addcom 7907 ax-mulcom 7908 ax-addass 7909 ax-mulass 7910 ax-distr 7911 ax-i2m1 7912 ax-0lt1 7913 ax-1rid 7914 ax-0id 7915 ax-rnegex 7916 ax-precex 7917 ax-cnre 7918 ax-pre-ltirr 7919 ax-pre-ltwlin 7920 ax-pre-lttrn 7921 ax-pre-apti 7922 ax-pre-ltadd 7923 ax-pre-mulgt0 7924 ax-pre-mulext 7925 |
| This theorem depends on definitions:
df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-nel 2443 df-ral 2460 df-rex 2461 df-reu 2462 df-rmo 2463 df-rab 2464 df-v 2739 df-sbc 2963 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4003 df-opab 4064 df-id 4292 df-po 4295 df-iso 4296 df-xp 4631 df-rel 4632 df-cnv 4633 df-co 4634 df-dm 4635 df-iota 5176 df-fun 5216 df-fv 5222 df-riota 5827 df-ov 5874 df-oprab 5875 df-mpo 5876 df-pnf 7989 df-mnf 7990 df-xr 7991 df-ltxr 7992 df-le 7993 df-sub 8125 df-neg 8126 df-reap 8527 df-ap 8534 df-div 8625 |
| This theorem is referenced by: rec11api
8705 rec11apd
8763 |
