Colors of
variables: wff
setvar class |
Syntax hints:
β wi 4 = wceq 1541
β wcel 2106 βcfv 6543 (class class class)co 7411
Basecbs 17146 βΎs
cress 17175 SubGrpcsubg 19002 SubRingcsubrg 20319 |
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 5299 ax-nul 5306 ax-pow 5363 ax-pr 5427 ax-un 7727 ax-cnex 11168 ax-1cn 11170 ax-addcl 11172 |
This theorem depends on definitions:
df-bi 206 df-an 397
df-or 846 df-3or 1088 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-reu 3377 df-rab 3433 df-v 3476 df-sbc 3778 df-csb 3894 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-pss 3967 df-nul 4323 df-if 4529 df-pw 4604 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-iun 4999 df-br 5149 df-opab 5211 df-mpt 5232 df-tr 5266 df-id 5574 df-eprel 5580 df-po 5588 df-so 5589 df-fr 5631 df-we 5633 df-xp 5682 df-rel 5683 df-cnv 5684 df-co 5685 df-dm 5686 df-rn 5687 df-res 5688 df-ima 5689 df-pred 6300 df-ord 6367 df-on 6368 df-lim 6369 df-suc 6370 df-iota 6495 df-fun 6545 df-fn 6546 df-f 6547 df-f1 6548 df-fo 6549 df-f1o 6550 df-fv 6551 df-ov 7414 df-oprab 7415 df-mpo 7416 df-om 7858 df-2nd 7978 df-frecs 8268 df-wrecs 8299 df-recs 8373 df-rdg 8412 df-nn 12215 df-sets 17099 df-slot 17117 df-ndx 17129 df-base 17147 df-ress 17176 df-subg 19005 df-ring 20060 df-subrg 20321 |
This theorem is referenced by: subrg1
20333 subrgmcl
20335 subrgdvds
20337 subrguss
20338 subrginv
20339 subrgdv
20340 subrgunit
20341 subsubrg
20349 issubdrg
20405 abvres
20451 qsssubdrg
21010 gzrngunitlem
21016 gzrngunit
21017 issubassa3
21426 sraassab
21428 sraassaOLD
21430 resspsrbas
21541 resspsradd
21542 resspsrmul
21543 resspsrvsca
21544 subrgpsr
21545 subrgascl
21633 subrgasclcl
21634 dmatcrng
22011 scmatcrng
22030 scmatstrbas
22035 sranlm
24208 isclmi
24600 plypf1
25733 sdrgdvcl
32438 sdrginvcl
32439 idlinsubrg
32594 evlsvvval
41217 evlsscaval
41218 evlsbagval
41220 evlsevl
41225 evlsmhpvvval
41249 mhphf
41251 |