| Colors of
variables: wff set class |
| Syntax hints:
→ wi 4 ∧ w3a 978
= wceq 1353 ∈
wcel 2148 ‘cfv 5218
(class class class)co 5877 Basecbs 12464
+gcplusg 12538 Mndcmnd 12822
Grpcgrp 12882 |
| This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709
ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4123 ax-pow 4176 ax-pr 4211 ax-un 4435 ax-cnex 7904 ax-resscn 7905 ax-1re 7907 ax-addrcl 7910 |
| This theorem depends on definitions:
df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2741 df-sbc 2965 df-un 3135 df-in 3137 df-ss 3144 df-pw 3579 df-sn 3600 df-pr 3601 df-op 3603 df-uni 3812 df-int 3847 df-br 4006 df-opab 4067 df-mpt 4068 df-id 4295 df-xp 4634 df-rel 4635 df-cnv 4636 df-co 4637 df-dm 4638 df-rn 4639 df-res 4640 df-iota 5180 df-fun 5220 df-fn 5221 df-fv 5226 df-ov 5880 df-inn 8922 df-2 8980 df-ndx 12467 df-slot 12468 df-base 12470 df-plusg 12551 df-mgm 12780 df-sgrp 12813 df-mnd 12823 df-grp 12885 |
| This theorem is referenced by: grpcld
12895 grprcan
12915 grprinv
12928 grpressid
12936 grplmulf1o
12949 grpinvadd
12953 grpsubf
12954 grpsubadd
12963 grpaddsubass
12965 grpnpcan
12967 grpsubsub4
12968 grppnpcan2
12969 grplactcnv
12977 mulgcl
13005 mulgaddcomlem
13011 mulgdir
13020 nmzsubg
13075 nsgid
13080 eqgcpbl
13092 ablsub4
13121 abladdsub4
13122 ringacl
13218 lmodacl
13394 lmodvacl
13397 rmodislmod
13446 |
