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 ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is used by:  anim1ci  341  dfco2a  5288  funco  5417  fliftval  6006  ltsrprg  8115  difelfznle  10553  nelfzo  10570  iseqf1olemqk  10959  ccatsymb  11386  pfxsuffeqwrdeq  11486  pfxccatin12lem2a  11515  difsqpwdvds  13140  resmhm  13847  mhmco  13850  rhmco  14565  resrhm  14640  gausslemma2dlem1a  16343  subusgr  16682  ex-ceil  16906