| Colors of
variables: wff
setvar class |
| Syntax hints:
→ wi 4 = wceq 1541
∈ wcel 2106 ‘cfv 6543 (class class class)co 7411
Ringcrg 20127 RingHom crh 20360
ℤringczring 21217 ℤRHomczrh 21268 |
| 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-rep 5285 ax-sep 5299 ax-nul 5306 ax-pow 5363 ax-pr 5427 ax-un 7727 ax-cnex 11168 ax-resscn 11169 ax-1cn 11170 ax-icn 11171 ax-addcl 11172 ax-addrcl 11173 ax-mulcl 11174 ax-mulrcl 11175 ax-mulcom 11176 ax-addass 11177 ax-mulass 11178 ax-distr 11179 ax-i2m1 11180 ax-1ne0 11181 ax-1rid 11182 ax-rnegex 11183 ax-rrecex 11184 ax-cnre 11185 ax-pre-lttri 11186 ax-pre-lttrn 11187 ax-pre-ltadd 11188 ax-pre-mulgt0 11189 ax-addf 11191 ax-mulf 11192 |
| 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-nel 3047 df-ral 3062 df-rex 3071 df-rmo 3376 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-tp 4633 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-riota 7367 df-ov 7414 df-oprab 7415 df-mpo 7416 df-om 7858 df-1st 7977 df-2nd 7978 df-frecs 8268 df-wrecs 8299 df-recs 8373 df-rdg 8412 df-1o 8468 df-er 8705 df-map 8824 df-en 8942 df-dom 8943 df-sdom 8944 df-fin 8945 df-pnf 11254 df-mnf 11255 df-xr 11256 df-ltxr 11257 df-le 11258 df-sub 11450 df-neg 11451 df-nn 12217 df-2 12279
df-3 12280 df-4 12281
df-5 12282 df-6 12283
df-7 12284 df-8 12285
df-9 12286 df-n0 12477 df-z 12563
df-dec 12682 df-uz 12827 df-fz 13489 df-seq 13971 df-struct 17084 df-sets 17101 df-slot 17119 df-ndx 17131 df-base 17149 df-ress 17178 df-plusg 17214 df-mulr 17215 df-starv 17216 df-tset 17220 df-ple 17221 df-ds 17223 df-unif 17224 df-0g 17391 df-mgm 18565 df-sgrp 18644 df-mnd 18660 df-mhm 18705 df-grp 18858 df-minusg 18859 df-mulg 18987 df-subg 19039 df-ghm 19128 df-cmn 19691 df-abl 19692 df-mgp 20029 df-rng 20047 df-ur 20076 df-ring 20129 df-cring 20130 df-rhm 20363 df-subrng 20434 df-subrg 20459 df-cnfld 21145 df-zring 21218 df-zrh 21272 |
| This theorem is referenced by: zrh1
21281 zrh0
21282 chrrhm
21302 domnchr
21303 zndvds0
21325 znf1o
21326 zzngim
21327 znfld
21335 znidomb
21336 znunit
21338 znrrg
21340 cygznlem3
21344 zrhpsgnmhm
21356 zrhpsgnodpm
21364 dchrzrhmul
26973 lgsqrlem1
27073 lgsqrlem2
27074 lgsqrlem3
27075 lgsdchr
27082 lgseisenlem3
27104 lgseisenlem4
27105 dchrisum0flblem1
27235 fermltlchr
32740 znfermltl
32741 elrspunidl
32808 ply1fermltlchr
32924 mdetpmtr1
33089 mdetpmtr12
33091 mdetlap
33098 zrhf1ker
33241 zrhunitpreima
33244 elzrhunit
33245 qqhval2lem
33247 qqhf
33252 qqhghm
33254 qqhrhm
33255 qqhnm
33256 |
