Metamath Proof Explorer


Theorem 3exp1

Description: Exportation from left triple conjunction. (Contributed by NM, 24-Feb-2005)

Ref Expression
Hypothesis 3exp1.1
|- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )
Assertion 3exp1
|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )

Proof

Step Hyp Ref Expression
1 3exp1.1
 |-  ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )
2 1 ex
 |-  ( ( ph /\ ps /\ ch ) -> ( th -> ta ) )
3 2 3exp
 |-  ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )