Colors of
variables: wff set class |
Syntax hints: wi 4
wa 104
wb 105 wceq 1353 wcel 2146 cfv 5208 (class class class)co 5865
cbs 12428
cplusg 12492 c0g 12626 cgrp 12738 cminusg 12739 |
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 1445 ax-7 1446 ax-gen 1447 ax-ie1 1491 ax-ie2 1492 ax-8 1502 ax-10 1503 ax-11 1504 ax-i12 1505 ax-bndl 1507 ax-4 1508 ax-17 1524 ax-i9 1528 ax-ial 1532 ax-i5r 1533 ax-13 2148 ax-14 2149 ax-ext 2157 ax-coll 4113 ax-sep 4116 ax-pow 4169 ax-pr 4203 ax-un 4427 ax-cnex 7877 ax-resscn 7878 ax-1re 7880 ax-addrcl 7883 |
This theorem depends on definitions:
df-bi 117 df-3an 980 df-tru 1356 df-nf 1459 df-sb 1761 df-eu 2027 df-mo 2028 df-clab 2162 df-cleq 2168 df-clel 2171 df-nfc 2306 df-ral 2458 df-rex 2459 df-reu 2460 df-rmo 2461 df-rab 2462 df-v 2737 df-sbc 2961 df-csb 3056 df-un 3131 df-in 3133 df-ss 3140 df-pw 3574 df-sn 3595 df-pr 3596 df-op 3598 df-uni 3806 df-int 3841 df-iun 3884 df-br 3999 df-opab 4060 df-mpt 4061 df-id 4287 df-xp 4626 df-rel 4627 df-cnv 4628 df-co 4629 df-dm 4630 df-rn 4631 df-res 4632 df-ima 4633 df-iota 5170 df-fun 5210 df-fn 5211 df-f 5212 df-f1 5213 df-fo 5214 df-f1o 5215 df-fv 5216 df-riota 5821 df-ov 5868 df-inn 8891 df-2 8949 df-ndx 12431 df-slot 12432 df-base 12434 df-plusg 12505 df-0g 12628 df-mgm 12640 df-sgrp 12673 df-mnd 12683 df-grp 12741 df-minusg 12742 |
This theorem is referenced by: grpinv11
12798 grpinvnz
12800 grpsubinv
12802 grpinvsub
12811 grpsubeq0
12815 grpnpcan
12821 mulgneg
12860 mulgnegneg
12861 mulginvinv
12867 mulgdir
12873 mulgass
12878 ablsub2inv
12910 |