Metamath Proof Explorer


Theorem exp44

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

Ref Expression
Hypothesis exp44.1
|- ( ( ph /\ ( ( ps /\ ch ) /\ th ) ) -> ta )
Assertion exp44
|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Proof

Step Hyp Ref Expression
1 exp44.1
 |-  ( ( ph /\ ( ( ps /\ ch ) /\ th ) ) -> ta )
2 1 exp32
 |-  ( ph -> ( ( ps /\ ch ) -> ( th -> ta ) ) )
3 2 expd
 |-  ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )