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Theorem com4l 84
Description: Commutation of antecedents. Rotate left. (Contributed by NM, 25-Apr-1994.) (Proof shortened by O'Cat, 15-Aug-2004.)
Hypothesis
Ref Expression
com4.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
Assertion
Ref Expression
com4l  |-  ( ps 
->  ( ch  ->  ( th  ->  ( ph  ->  ta ) ) ) )

Proof of Theorem com4l
StepHypRef Expression
1 com4.1 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
21com3l 81 . 2  |-  ( ps 
->  ( ch  ->  ( ph  ->  ( th  ->  ta ) ) ) )
32com34 83 1  |-  ( ps 
->  ( ch  ->  ( th  ->  ( ph  ->  ta ) ) ) )
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:  com4t  85  com4r  86  com14  88  com5l  92  3impd  1199  facwordi  10479  fiinopn  12160
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