Theorem anim12ci 337

Description: Variant of anim12i 336 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 336	. 2 |- ( ( ch /\ ph ) -> ( th /\ ps ) )
4	3	ancoms 266	1 |- ( ( ph /\ ch ) -> ( th /\ ps ) )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by:  anim1ci  339  dfco2a  5111  funco  5238  fliftval  5779  ltsrprg  7709  difelfznle  10091  iseqf1olemqk  10450  difsqpwdvds  12291  mhmco  12705  ex-ceil  13761