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Theorem com15 93
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 92 . 2 |- ( ps -> ( ch -> ( th -> ( ta -> ( ph -> et ) ) ) ) )
32com4r 86 1 |- ( ta -> ( ps -> ( ch -> ( th -> ( ph -> et ) ) ) ) )
Colors of variables: wff set class
Syntax hints:   -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7
This theorem is referenced by: (None)
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