Theorem anim12ci 339

Description: Variant of anim12i 338 with commutation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)

Hypotheses

Ref	Expression
anim12i.1	|- ( ph -> ps )
anim12i.2	|- ( ch -> th )

Assertion

Ref	Expression
anim12ci	|- ( ( ph /\ ch ) -> ( th /\ ps ) )

Proof of Theorem anim12ci

Step	Hyp	Ref	Expression
1		anim12i.2	. . 3 |- ( ch -> th )
2		anim12i.1	. . 3 |- ( ph -> ps )
3	1, 2	anim12i 338	. 2 |- ( ( ch /\ ph ) -> ( th /\ ps ) )
4	3	ancoms 268	1 |- ( ( ph /\ ch ) -> ( th /\ ps ) )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  anim1ci  341  dfco2a  5237  funco  5366  fliftval  5940  ltsrprg  7966  difelfznle  10369  nelfzo  10386  iseqf1olemqk  10768  ccatsymb  11178  pfxsuffeqwrdeq  11278  pfxccatin12lem2a  11307  difsqpwdvds  12910  resmhm  13569  mhmco  13572  rhmco  14187  resrhm  14261  gausslemma2dlem1a  15786  subusgr  16125  ex-ceil  16322