Theorem anim12ci 332

Description: Variant of anim12i 331 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 331	. 2 |- ( ( ch /\ ph ) -> ( th /\ ps ) )
4	3	ancoms 264	1 |- ( ( ph /\ ch ) -> ( th /\ ps ) )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem is referenced by:  dfco2a  4841  funco  4960  fliftval  5460  ltsrprg  6924  difelfznle  9146  ex-ceil  10564