Metamath Proof Explorer


Theorem exp41

Description: An exportation inference. (Contributed by NM, 26-Apr-1994)

Ref Expression
Hypothesis exp41.1
|- ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )
Assertion exp41
|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Proof

Step Hyp Ref Expression
1 exp41.1
 |-  ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) -> ta )
2 1 ex
 |-  ( ( ( ph /\ ps ) /\ ch ) -> ( th -> ta ) )
3 2 exp31
 |-  ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )