MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  com5l Unicode version

Theorem com5l 86
Description: Commutation of antecedents. Rotate left. (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
com5l  |-  ( ps 
->  ( ch  ->  ( th  ->  ( ta  ->  (
ph  ->  et ) ) ) ) )

Proof of Theorem com5l
StepHypRef Expression
1 com5.1 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
21com4l 78 . 2  |-  ( ps 
->  ( ch  ->  ( th  ->  ( ph  ->  ( ta  ->  et )
) ) ) )
32com45 83 1  |-  ( ps 
->  ( ch  ->  ( th  ->  ( ta  ->  (
ph  ->  et ) ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  com15  87  com52l  88  com52r  89  cmptdst  25568  limptlimpr2lem2  25575  lemindclsbu  25995  clscnc  26010
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
  Copyright terms: Public domain W3C validator