Metamath Proof Explorer


Theorem com4l

Description: Commutation of antecedents. Rotate left. (Contributed by NM, 25-Apr-1994) (Proof shortened by Mel L. O'Cat, 15-Aug-2004)

Ref Expression
Hypothesis com4.1
|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
Assertion com4l
|- ( ps -> ( ch -> ( th -> ( ph -> ta ) ) ) )

Proof

Step Hyp Ref Expression
1 com4.1
 |-  ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2 1 com3l
 |-  ( ps -> ( ch -> ( ph -> ( th -> ta ) ) ) )
3 2 com34
 |-  ( ps -> ( ch -> ( th -> ( ph -> ta ) ) ) )