Colors of
variables: wff
setvar class |
Syntax hints:
→ wi 4 ∈ wcel 2099
Grpcgrp 18890 Rngcrng 20092 |
This theorem was proved from axioms:
ax-mp 5 ax-1 6 ax-2 7
ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906
ax-6 1964 ax-7 2004 ax-8 2101
ax-9 2109 ax-ext 2699 ax-nul 5306 |
This theorem depends on definitions:
df-bi 206 df-an 396
df-or 847 df-3an 1087 df-tru 1537 df-fal 1547 df-ex 1775 df-sb 2061 df-clab 2706 df-cleq 2720 df-clel 2806 df-ne 2938 df-ral 3059 df-rab 3430 df-v 3473 df-sbc 3777 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-nul 4324 df-if 4530 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4909 df-br 5149 df-iota 6500 df-fv 6556 df-ov 7423 df-abl 19738 df-rng 20093 |
This theorem is referenced by: rngacl
20102 rng0cl
20103 rngrz
20106 rngmneg1
20107 rngmneg2
20108 rngm2neg
20109 rngsubdi
20111 rngsubdir
20112 prdsrngd
20116 subrngsubg
20489 cntzsubrng
20504 rnglidlmcl
21112 rnglidl0
21125 rnglidl1
21128 2idlcpblrng
21165 rngqiprngimfolem
21180 rngqiprngimf1lem
21184 rngqiprngghm
21189 rngqiprngimf1
21190 rngqiprngimfo
21191 rngqiprngfulem3
21203 rngqiprngfulem4
21204 rngqiprngfulem5
21205 pzriprnglem4
21410 pzriprnglem10
21416 |