Metamath Proof Explorer


Theorem 3exp2

Description: Exportation from right triple conjunction. (Contributed by NM, 26-Oct-2006)

Ref Expression
Hypothesis 3exp2.1
|- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )
Assertion 3exp2
|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Proof

Step Hyp Ref Expression
1 3exp2.1
 |-  ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )
2 1 ex
 |-  ( ph -> ( ( ps /\ ch /\ th ) -> ta ) )
3 2 3expd
 |-  ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )