Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 = wceq 1542
∈ wcel 2107 ⊆
wss 3911 ‘cfv 6497
Basecbs 17088 LSubSpclss 20407
ringLModcrglmod 20646 LIdealclidl 20647 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914
ax-6 1972 ax-7 2012 ax-8 2109
ax-9 2117 ax-10 2138 ax-11 2155 ax-12 2172 ax-ext 2704 ax-rep 5243 ax-sep 5257 ax-nul 5264 ax-pow 5321 ax-pr 5385 ax-un 7673 ax-cnex 11112 ax-resscn 11113 ax-1cn 11114 ax-icn 11115 ax-addcl 11116 ax-addrcl 11117 ax-mulcl 11118 ax-mulrcl 11119 ax-mulcom 11120 ax-addass 11121 ax-mulass 11122 ax-distr 11123 ax-i2m1 11124 ax-1ne0 11125 ax-1rid 11126 ax-rnegex 11127 ax-rrecex 11128 ax-cnre 11129 ax-pre-lttri 11130 ax-pre-lttrn 11131 ax-pre-ltadd 11132 ax-pre-mulgt0 11133 |
This theorem depends on definitions:
df-bi 206 df-an 398
df-or 847 df-3or 1089 df-3an 1090 df-tru 1545 df-fal 1555 df-ex 1783 df-nf 1787 df-sb 2069 df-mo 2535 df-eu 2564 df-clab 2711 df-cleq 2725 df-clel 2811 df-nfc 2886 df-ne 2941 df-nel 3047 df-ral 3062 df-rex 3071 df-reu 3353 df-rab 3407 df-v 3446 df-sbc 3741 df-csb 3857 df-dif 3914 df-un 3916 df-in 3918 df-ss 3928 df-pss 3930 df-nul 4284 df-if 4488 df-pw 4563 df-sn 4588 df-pr 4590 df-op 4594 df-uni 4867 df-iun 4957 df-br 5107 df-opab 5169 df-mpt 5190 df-tr 5224 df-id 5532 df-eprel 5538 df-po 5546 df-so 5547 df-fr 5589 df-we 5591 df-xp 5640 df-rel 5641 df-cnv 5642 df-co 5643 df-dm 5644 df-rn 5645 df-res 5646 df-ima 5647 df-pred 6254 df-ord 6321 df-on 6322 df-lim 6323 df-suc 6324 df-iota 6449 df-fun 6499 df-fn 6500 df-f 6501 df-f1 6502 df-fo 6503 df-f1o 6504 df-fv 6505 df-riota 7314 df-ov 7361 df-oprab 7362 df-mpo 7363 df-om 7804 df-2nd 7923 df-frecs 8213 df-wrecs 8244 df-recs 8318 df-rdg 8357 df-er 8651 df-en 8887 df-dom 8888 df-sdom 8889 df-pnf 11196 df-mnf 11197 df-xr 11198 df-ltxr 11199 df-le 11200 df-sub 11392 df-neg 11393 df-nn 12159 df-2 12221
df-3 12222 df-4 12223
df-5 12224 df-6 12225
df-7 12226 df-8 12227
df-sets 17041 df-slot 17059 df-ndx 17071 df-base 17089 df-sca 17154 df-vsca 17155 df-ip 17156 df-lss 20408 df-sra 20649 df-rgmod 20650 df-lidl 20651 |
This theorem is referenced by: lidlsubg
20701 lidl1el
20704 drngnidl
20715 2idlcpbl
20720 lpigen
20742 zringlpirlem1
20899 zringlpirlem3
20901 zndvds
20972 ig1peu
25552 ig1pdvds
25557 ig1prsp
25558 ply1lpir
25559 rspidlid
32210 ringlsmss1
32225 ringlsmss2
32226 lsmidl
32230 intlidl
32247 0ringidl
32250 elrspunidl
32251 rhmimaidl
32254 prmidl2
32261 idlmulssprm
32262 mxidlprm
32285 ssmxidllem
32286 idlsrgmulrcl
32300 idlsrgmulrss1
32301 idlsrgmulrss2
32302 zarcls1
32507 zarclsun
32508 zarclsiin
32509 zarclsint
32510 zarcmplem
32519 rhmpreimacnlem
32522 hbtlem2
41494 hbtlem4
41496 hbtlem5
41498 hbtlem6
41499 hbt
41500 lidldomn1
46305 lidlbas
46307 |