MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  com5r Structured version   Visualization version   Unicode version
Theorem com5r 104
Description: Commutation of antecedents. Rotate right. (Contributed by Wolf Lammen, 29-Jul-2012.)
Hypothesis
Ref Expression
com5.1 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
Assertion
Ref Expression
com5r |- ( ta -> ( ph -> ( ps -> ( ch -> ( th -> et ) ) ) ) )
Proof of Theorem com5r
StepHypRef Expression
1 com5.1 . . 3 |- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
21com52l 102 . 2 |- ( ch -> ( th -> ( ta -> ( ph -> ( ps -> et ) ) ) ) )
32com52l 102 1 |- ( ta -> ( ph -> ( ps -> ( ch -> ( th -> et ) ) ) ) )
Colors of variables: wff setvar 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:  ad5ant234  1308  ad5ant235  1309
  Copyright terms: Public domain W3C validator