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Theorem com3l 81
Description: Commutation of antecedents. Rotate left. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 28-Jul-2012.)
Hypothesis
Ref Expression
com3.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
Assertion
Ref Expression
com3l  |-  ( ps 
->  ( ch  ->  ( ph  ->  th ) ) )

Proof of Theorem com3l
StepHypRef Expression
1 com3.1 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
21com3r 79 . 2  |-  ( ch 
->  ( ph  ->  ( ps  ->  th ) ) )
32com3r 79 1  |-  ( ps 
->  ( ch  ->  ( ph  ->  th ) ) )
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:  com4l  84  impd  252  expdcom  1401  nebidc  2363  sbcimdv  2944  prel12  3666  reusv3  4349  relcoi1  5038  oprabid  5769  poxp  6095  reldmtpos  6116  tfrlem9  6182  tfri3  6230  ordiso2  6886  distrlem5prl  7358  distrlem5pru  7359  bndndx  8927  uzind2  9114  leexp1a  10288  cncongr1  11680  bj-inf2vnlem2  12980
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