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  8114  difelfznle  10552  nelfzo  10569  iseqf1olemqk  10957  ccatsymb  11384  pfxsuffeqwrdeq  11484  pfxccatin12lem2a  11513  difsqpwdvds  13137  resmhm  13843  mhmco  13846  rhmco  14530  resrhm  14605  gausslemma2dlem1a  16275  subusgr  16614  ex-ceil  16838