Metamath Proof Explorer

Theorem com5l

Description: Commutation of antecedents. Rotate left. (Contributed by Jeff Hankins, 28-Jun-2009) (Proof shortened by Wolf Lammen, 29-Jul-2012)

Ref Expression
Hypothesis com5.1 
|- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
Assertion com5l 
|- ( ps -> ( ch -> ( th -> ( ta -> ( ph -> et ) ) ) ) )

Proof

Step Hyp Ref Expression
1 com5.1 
 |-  ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )
2 1 com4l 
 |-  ( ps -> ( ch -> ( th -> ( ph -> ( ta -> et ) ) ) ) )
3 2 com45 
 |-  ( ps -> ( ch -> ( th -> ( ta -> ( ph -> et ) ) ) ) )