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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
StepHypRef Expression
1 anim12i.2 . . 3  |-  ( ch 
->  th )
2 anim12i.1 . . 3  |-  ( ph  ->  ps )
31, 2anim12i 331 . 2  |-  ( ( ch  /\  ph )  ->  ( th  /\  ps ) )
43ancoms 264 1  |-  ( (
ph  /\  ch )  ->  ( th  /\  ps ) )
Colors of variables: wff set class
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  4872  funco  4991  fliftval  5493  ltsrprg  7063  difelfznle  9300  ex-ceil  10849
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