Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∧ wa 396
= wceq 1541 ∈
wcel 2106 ‘cfv 6540
(class class class)co 7405 Basecbs 17140
+gcplusg 17193 0gc0g 17381 Mndcmnd 18621 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913
ax-6 1971 ax-7 2011 ax-8 2108
ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2703 ax-sep 5298 ax-nul 5305 ax-pr 5426 |
This theorem depends on definitions:
df-bi 206 df-an 397
df-or 846 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2534 df-eu 2563 df-clab 2710 df-cleq 2724 df-clel 2810 df-nfc 2885 df-ne 2941 df-ral 3062 df-rex 3071 df-rmo 3376 df-reu 3377 df-rab 3433 df-v 3476 df-sbc 3777 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-iota 6492 df-fun 6542 df-fv 6548 df-riota 7361 df-ov 7408 df-0g 17383 df-mgm 18557 df-sgrp 18606 df-mnd 18622 |
This theorem is referenced by: mndpfo
18644 issubmnd
18648 ress0g
18649 submnd0
18650 mndinvmod
18651 prdsidlem
18653 imasmnd
18659 xpsmnd0
18662 mndind
18705 gsumccat
18718 grprid
18849 mhmid
18940 mhmmnd
18941 mulgnn0dir
18978 cntzsubm
19196 oppgmnd
19215 lsmub1x
19508 gsumval3
19769 gsumzsplit
19789 srgbinomlem3
20044 mndvrid
21887 mndifsplit
22129 gsummatr01
22152 smadiadet
22163 pmatcollpw3fi1lem1
22279 chfacfscmulgsum
22353 chfacfpmmulgsum
22357 tsmssplit
23647 tsmsxp
23650 gsummptres
32191 gsummptres2
32192 cntzsnid
32200 slmd0vrid
32355 mndtccatid
47666 |