Metamath Proof Explorer


Theorem com14

Description: Commutation of antecedents. Swap 1st and 4th. (Contributed by NM, 25-Apr-1994) (Proof shortened by Wolf Lammen, 28-Jul-2012)

Ref Expression
Hypothesis com4.1
|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
Assertion com14
|- ( th -> ( ps -> ( ch -> ( ph -> ta ) ) ) )

Proof

Step Hyp Ref Expression
1 com4.1
 |-  ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2 1 com4l
 |-  ( ps -> ( ch -> ( th -> ( ph -> ta ) ) ) )
3 2 com3r
 |-  ( th -> ( ps -> ( ch -> ( ph -> ta ) ) ) )