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Theorem com45 83
Description: Commutation of antecedents. Swap 4th and 5th. (Contributed by Jeff Hankins, 28-Jun-2009.)
Hypothesis
Ref Expression
com5.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
Assertion
Ref Expression
com45  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ta  ->  ( th  ->  et )
) ) ) )

Proof of Theorem com45
StepHypRef Expression
1 com5.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
2 pm2.04 76 . 2  |-  ( ( th  ->  ( ta  ->  et ) )  -> 
( ta  ->  ( th  ->  et ) ) )
31, 2syl8 65 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ta  ->  ( th  ->  et )
) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  com35  84  com25  85  com5l  86  islmhm2  15795  dfon2lem8  24146
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
  Copyright terms: Public domain W3C validator