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  5237  funco  5366  fliftval  5941  ltsrprg  7967  difelfznle  10370  nelfzo  10387  iseqf1olemqk  10770  ccatsymb  11183  pfxsuffeqwrdeq  11283  pfxccatin12lem2a  11312  difsqpwdvds  12929  resmhm  13588  mhmco  13591  rhmco  14207  resrhm  14281  gausslemma2dlem1a  15806  subusgr  16145  ex-ceil  16369