Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 = wceq 1541
∈ wcel 2106 ran crn 5631
‘cfv 6491 1st
c1st 7909 GrpOpcgr 29229
GIdcgi 29230 RingOpscrngo 36248 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913
ax-6 1971 ax-7 2011 ax-8 2108
ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2708 ax-sep 5254 ax-nul 5261 ax-pr 5382 ax-un 7662 |
This theorem depends on definitions:
df-bi 206 df-an 397
df-or 846 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2539 df-eu 2568 df-clab 2715 df-cleq 2729 df-clel 2815 df-nfc 2887 df-ne 2942 df-ral 3063 df-rex 3072 df-reu 3352 df-rab 3406 df-v 3445 df-sbc 3738 df-csb 3854 df-dif 3911 df-un 3913 df-in 3915 df-ss 3925 df-nul 4281 df-if 4485 df-sn 4585 df-pr 4587 df-op 4591 df-uni 4864 df-iun 4954 df-br 5104 df-opab 5166 df-mpt 5187 df-id 5528 df-xp 5636 df-rel 5637 df-cnv 5638 df-co 5639 df-dm 5640 df-rn 5641 df-iota 6443 df-fun 6493 df-fn 6494 df-f 6495 df-fo 6497 df-fv 6499 df-riota 7305 df-ov 7352 df-1st 7911 df-2nd 7912 df-grpo 29233 df-gid 29234 df-ablo 29285 df-rngo 36249 |
This theorem is referenced by: rngolz
36276 rngorz
36277 rngosn6
36280 rngoueqz
36294 rngoidl
36378 0idl
36379 keridl
36386 prnc
36421 isdmn3
36428 |