Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∧ w3a 1085
= wceq 1539 ∈
wcel 2104 × cxp 5673
ran crn 5676 ⟶wf 6538
‘cfv 6542 (class class class)co 7411
1st c1st 7975
2nd c2nd 7976
RingOpscrngo 37065 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1911
ax-6 1969 ax-7 2009 ax-8 2106
ax-9 2114 ax-10 2135 ax-11 2152 ax-12 2169 ax-ext 2701 ax-sep 5298 ax-nul 5305 ax-pr 5426 ax-un 7727 |
This theorem depends on definitions:
df-bi 206 df-an 395
df-or 844 df-3an 1087 df-tru 1542 df-fal 1552 df-ex 1780 df-nf 1784 df-sb 2066 df-mo 2532 df-eu 2561 df-clab 2708 df-cleq 2722 df-clel 2808 df-nfc 2883 df-ne 2939 df-ral 3060 df-rex 3069 df-rab 3431 df-v 3474 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-nul 4322 df-if 4528 df-sn 4628 df-pr 4630 df-op 4634 df-uni 4908 df-br 5148 df-opab 5210 df-mpt 5231 df-id 5573 df-xp 5681 df-rel 5682 df-cnv 5683 df-co 5684 df-dm 5685 df-rn 5686 df-iota 6494 df-fun 6544 df-fn 6545 df-f 6546 df-fv 6550 df-ov 7414 df-1st 7977 df-2nd 7978 df-rngo 37066 |
This theorem is referenced by: rngolz
37093 rngorz
37094 rngonegmn1l
37112 rngonegmn1r
37113 rngoneglmul
37114 rngonegrmul
37115 rngosubdi
37116 rngosubdir
37117 isdrngo2
37129 rngohomco
37145 rngoisocnv
37152 crngm4
37174 rngoidl
37195 keridl
37203 prnc
37238 ispridlc
37241 pridlc3
37244 dmncan1
37247 |