Metamath Proof Explorer

Theorem exp520

Description: A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009)

Ref Expression
Hypothesis exp520.1 
|- ( ( ( ph /\ ps /\ ch ) /\ ( th /\ ta ) ) -> et )
Assertion exp520 
|- ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )

Proof

Step Hyp Ref Expression
1 exp520.1 
 |-  ( ( ( ph /\ ps /\ ch ) /\ ( th /\ ta ) ) -> et )
2 1 ex 
 |-  ( ( ph /\ ps /\ ch ) -> ( ( th /\ ta ) -> et ) )
3 2 exp5o 
 |-  ( ph -> ( ps -> ( ch -> ( th -> ( ta -> et ) ) ) ) )