Metamath Proof Explorer


Theorem exp43

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

Ref Expression
Hypothesis exp43.1
|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) -> ta )
Assertion exp43
|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Proof

Step Hyp Ref Expression
1 exp43.1
 |-  ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) -> ta )
2 1 ex
 |-  ( ( ph /\ ps ) -> ( ( ch /\ th ) -> ta ) )
3 2 exp4b
 |-  ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )