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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
StepHypRef Expression
1 anim12i.2 . . 3  |-  ( ch 
->  th )
2 anim12i.1 . . 3  |-  ( ph  ->  ps )
31, 2anim12i 336 . 2  |-  ( ( ch  /\  ph )  ->  ( th  /\  ps ) )
43ancoms 266 1  |-  ( (
ph  /\  ch )  ->  ( th  /\  ps ) )
Colors of variables: wff set class
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  5086  funco  5210  fliftval  5750  ltsrprg  7667  difelfznle  10034  iseqf1olemqk  10393  ex-ceil  13302
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