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Theorem com15 87
Description: Commutation of antecedents. Swap 1st and 5th. (Contributed by Jeff Hankins, 28-Jun-2009.) (Proof shortened by Wolf Lammen, 29-Jul-2012.)
Hypothesis
Ref Expression
com5.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
Assertion
Ref Expression
com15  |-  ( ta 
->  ( ps  ->  ( ch  ->  ( th  ->  (
ph  ->  et ) ) ) ) )

Proof of Theorem com15
StepHypRef Expression
1 com5.1 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
21com5l 86 . 2  |-  ( ps 
->  ( ch  ->  ( th  ->  ( ta  ->  (
ph  ->  et ) ) ) ) )
32com4r 80 1  |-  ( ta 
->  ( ps  ->  ( ch  ->  ( th  ->  (
ph  ->  et ) ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  zerdivemp1  25436  zerdivemp1x  26586
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
  Copyright terms: Public domain W3C validator