Colors of
variables: wff set class |
Syntax hints: wi 4
wa 104
wcel 2148
wne 2347
c0 3423
com 4590
(class class class)co 5875 comu 6415 cnpi 7271 cmi 7273 |
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-coll 4119 ax-sep 4122 ax-nul 4130 ax-pow 4175 ax-pr 4210 ax-un 4434 ax-setind 4537 ax-iinf 4588 |
This theorem depends on definitions:
df-bi 117 df-dc 835
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-ral 2460 df-rex 2461 df-reu 2462 df-rab 2464 df-v 2740 df-sbc 2964 df-csb 3059 df-dif 3132 df-un 3134 df-in 3136 df-ss 3143 df-nul 3424 df-pw 3578 df-sn 3599 df-pr 3600 df-op 3602 df-uni 3811 df-int 3846 df-iun 3889 df-br 4005 df-opab 4066 df-mpt 4067 df-tr 4103 df-id 4294 df-iord 4367 df-on 4369 df-suc 4372 df-iom 4591 df-xp 4633 df-rel 4634 df-cnv 4635 df-co 4636 df-dm 4637 df-rn 4638 df-res 4639 df-ima 4640 df-iota 5179 df-fun 5219 df-fn 5220 df-f 5221 df-f1 5222 df-fo 5223 df-f1o 5224 df-fv 5225 df-ov 5878 df-oprab 5879 df-mpo 5880 df-1st 6141 df-2nd 6142 df-recs 6306 df-irdg 6371 df-oadd 6421 df-omul 6422 df-ni 7303 df-mi 7305 |
This theorem is referenced by: mulasspig
7331 distrpig
7332 ltmpig
7338 enqer
7357 enqdc
7360 addcmpblnq
7366 mulcmpblnq
7367 addpipqqslem
7368 mulpipq2
7370 mulpipqqs
7372 ordpipqqs
7373 addclnq
7374 mulclnq
7375 addcomnqg
7380 addassnqg
7381 mulassnqg
7383 mulcanenq
7384 distrnqg
7386 recexnq
7389 nqtri3or
7395 ltdcnq
7396 ltsonq
7397 ltanqg
7399 ltmnqg
7400 1lt2nq
7405 ltexnqq
7407 archnqq
7416 addcmpblnq0
7442 mulcmpblnq0
7443 mulcanenq0ec
7444 addclnq0
7450 mulclnq0
7451 nqpnq0nq
7452 nqnq0a
7453 nqnq0m
7454 nq0m0r
7455 distrnq0
7458 addassnq0lemcl
7460 |