Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∧ w3a 1088
= wceq 1542 ∈
wcel 2107 × cxp 5675
ran crn 5678 ⟶wf 6540
‘cfv 6544 (class class class)co 7409
1st c1st 7973
2nd c2nd 7974
RingOpscrngo 36762 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914
ax-6 1972 ax-7 2012 ax-8 2109
ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 ax-sep 5300 ax-nul 5307 ax-pr 5428 ax-un 7725 |
This theorem depends on definitions:
df-bi 206 df-an 398
df-or 847 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ne 2942 df-ral 3063 df-rex 3072 df-rab 3434 df-v 3477 df-dif 3952 df-un 3954 df-in 3956 df-ss 3966 df-nul 4324 df-if 4530 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4910 df-br 5150 df-opab 5212 df-mpt 5233 df-id 5575 df-xp 5683 df-rel 5684 df-cnv 5685 df-co 5686 df-dm 5687 df-rn 5688 df-iota 6496 df-fun 6546 df-fn 6547 df-f 6548 df-fv 6552 df-ov 7412 df-1st 7975 df-2nd 7976 df-rngo 36763 |
This theorem is referenced by: rngolz
36790 rngorz
36791 rngonegmn1l
36809 rngonegmn1r
36810 rngoneglmul
36811 rngonegrmul
36812 rngosubdi
36813 rngosubdir
36814 isdrngo2
36826 rngohomco
36842 rngoisocnv
36849 crngm4
36871 rngoidl
36892 keridl
36900 prnc
36935 ispridlc
36938 pridlc3
36941 dmncan1
36944 |