Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∧ w3a 1088
= wceq 1542 ∈
wcel 2107 ‘cfv 6500
(class class class)co 7361 Basecbs 17091
+gcplusg 17141 Grpcgrp 18756
Ringcrg 19972 |
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-ext 2704 ax-nul 5267 |
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-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-ne 2941 df-ral 3062 df-rex 3071 df-rab 3407 df-v 3449 df-sbc 3744 df-dif 3917 df-un 3919 df-in 3921 df-ss 3931 df-nul 4287 df-if 4491 df-sn 4591 df-pr 4593 df-op 4597 df-uni 4870 df-br 5110 df-iota 6452 df-fv 6508 df-ov 7364 df-mgm 18505 df-sgrp 18554 df-mnd 18565 df-grp 18759 df-ring 19974 |
This theorem is referenced by: ringcomlem
20008 ringcom
20009 ringlghm
20036 ringrghm
20037 imasring
20053 qusring2
20054 cntzsubr
20298 srngadd
20359 issrngd
20363 lmodprop2d
20428 prdslmodd
20474 ip2subdi
21071 psrlmod
21393 mpfind
21540 coe1add
21658 mat1ghm
21855 scmatghm
21905 mdetrlin2
21979 mdetunilem5
21988 cpmatacl
22088 mdegaddle
25462 deg1addle2
25490 deg1add
25491 ply1divex
25524 frobrhm
32124 rhmpreimaidl
32255 dvhlveclem
39621 baerlem3lem1
40220 mendlmod
41567 cznrng
46343 lmod1lem3
46660 |