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Theorem com25 85
Description: Commutation of antecedents. Swap 2nd and 5th. (Contributed by Jeff Hankins, 28-Jun-2009.)
Hypothesis
Ref Expression
com5.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
Assertion
Ref Expression
com25  |-  ( ph  ->  ( ta  ->  ( ch  ->  ( th  ->  ( ps  ->  et )
) ) ) )

Proof of Theorem com25
StepHypRef Expression
1 com5.1 . . . 4  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
21com24 81 . . 3  |-  ( ph  ->  ( th  ->  ( ch  ->  ( ps  ->  ( ta  ->  et )
) ) ) )
32com45 83 . 2  |-  ( ph  ->  ( th  ->  ( ch  ->  ( ta  ->  ( ps  ->  et )
) ) ) )
43com24 81 1  |-  ( ph  ->  ( ta  ->  ( ch  ->  ( th  ->  ( ps  ->  et )
) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  neindisj2  16876  2ndcdisj  17198  oriso  25317  zerdivemp1  25539  limptlimpr2lem2  25678  distsava  25792  clscnc  26113  lppotos  26247  zerdivemp1x  26689  injresinjlem  28214
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
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