Colors of
variables: wff set class |
Syntax hints:
→ wi 4 ∧ wa 104
= wceq 1353 ∈
wcel 2148 ∀wral 2455
∃wrex 2456 ‘cfv 5214 (class class class)co 5871
Basecbs 12453 +gcplusg 12527 Mndcmnd 12748 |
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 4120 ax-pow 4173 ax-pr 4208 ax-un 4432 ax-cnex 7898 ax-resscn 7899 ax-1re 7901 ax-addrcl 7904 |
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 2739 df-sbc 2963 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-int 3845 df-br 4003 df-opab 4064 df-mpt 4065 df-id 4292 df-xp 4631 df-rel 4632 df-cnv 4633 df-co 4634 df-dm 4635 df-rn 4636 df-res 4637 df-iota 5176 df-fun 5216 df-fn 5217 df-fv 5222 df-ov 5874 df-inn 8915 df-2 8973 df-ndx 12456 df-slot 12457 df-base 12459 df-plusg 12540 df-mgm 12706 df-sgrp 12739 df-mnd 12749 |
This theorem is referenced by: mndideu
12758 mndidcl
12762 mndlrid
12766 |