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Theorem com14 87
Description: Commutation of antecedents. Swap 1st and 4th. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 28-Jul-2012.)
Hypothesis
Ref Expression
com4.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
Assertion
Ref Expression
com14  |-  ( th 
->  ( ps  ->  ( ch  ->  ( ph  ->  ta ) ) ) )

Proof of Theorem com14
StepHypRef Expression
1 com4.1 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
21com4l 83 . 2  |-  ( ps 
->  ( ch  ->  ( th  ->  ( ph  ->  ta ) ) ) )
32com3r 78 1  |-  ( th 
->  ( ps  ->  ( ch  ->  ( ph  ->  ta ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7
This theorem is referenced by:  f1o2ndf1  5928  fz0fzdiffz0  9432  elfzodifsumelfzo  9501  ssfzo12  9524  dfgcd2  10783  cncongr1  10865
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