Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∧ wa 395
= wceq 1534 ∈
wcel 2099 ran crn 5673
‘cfv 6542 (class class class)co 7414
1st c1st 7985
2nd c2nd 7986
GIdcgi 30293 RingOpscrngo 37361 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906
ax-6 1964 ax-7 2004 ax-8 2101
ax-9 2109 ax-10 2130 ax-11 2147 ax-12 2167 ax-ext 2699 ax-sep 5293 ax-nul 5300 ax-pr 5423 ax-un 7734 |
This theorem depends on definitions:
df-bi 206 df-an 396
df-or 847 df-3an 1087 df-tru 1537 df-fal 1547 df-ex 1775 df-nf 1779 df-sb 2061 df-mo 2530 df-eu 2559 df-clab 2706 df-cleq 2720 df-clel 2806 df-nfc 2881 df-ne 2937 df-ral 3058 df-rex 3067 df-rmo 3372 df-reu 3373 df-rab 3429 df-v 3472 df-sbc 3776 df-csb 3891 df-dif 3948 df-un 3950 df-in 3952 df-ss 3962 df-nul 4319 df-if 4525 df-sn 4625 df-pr 4627 df-op 4631 df-uni 4904 df-iun 4993 df-br 5143 df-opab 5205 df-mpt 5226 df-id 5570 df-xp 5678 df-rel 5679 df-cnv 5680 df-co 5681 df-dm 5682 df-rn 5683 df-iota 6494 df-fun 6544 df-fn 6545 df-f 6546 df-fo 6548 df-fv 6550 df-riota 7370 df-ov 7417 df-1st 7987 df-2nd 7988 df-grpo 30296 df-gid 30297 df-ablo 30348 df-ass 37310 df-exid 37312 df-mgmOLD 37316 df-sgrOLD 37328 df-mndo 37334 df-rngo 37362 |
This theorem is referenced by: rngonegmn1l
37408 zerdivemp1x
37414 isdrngo2
37425 1idl
37493 smprngopr
37519 prnc
37534 |