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  5229  funco  5358  fliftval  5930  ltsrprg  7945  difelfznle  10343  nelfzo  10360  iseqf1olemqk  10741  ccatsymb  11150  pfxsuffeqwrdeq  11245  pfxccatin12lem2a  11274  difsqpwdvds  12876  resmhm  13535  mhmco  13538  rhmco  14153  resrhm  14227  gausslemma2dlem1a  15752  ex-ceil  16145