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Theorem com24 87
Description: Commutation of antecedents. Swap 2nd 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
com24  |-  ( ph  ->  ( th  ->  ( ch  ->  ( ps  ->  ta ) ) ) )

Proof of Theorem com24
StepHypRef Expression
1 com4.1 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
21com4t 85 . 2  |-  ( ch 
->  ( th  ->  ( ph  ->  ( ps  ->  ta ) ) ) )
32com13 80 1  |-  ( ph  ->  ( th  ->  ( ch  ->  ( ps  ->  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:  com25  91  tfrlem9  6296  nnmordi  6493  fundmen  6782  fiintim  6904  elfzodifsumelfzo  10150  ssfzo12  10173  dvdsmodexp  11750  infpnlem1  12304  grpinveu  12734  cnpnei  12978
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