Metamath Proof Explorer

Theorem 3expd

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

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

Proof

Step Hyp Ref Expression
1 3expd.1 
 |-  ( ph -> ( ( ps /\ ch /\ th ) -> ta ) )
2 1 com12 
 |-  ( ( ps /\ ch /\ th ) -> ( ph -> ta ) )
3 2 3exp 
 |-  ( ps -> ( ch -> ( th -> ( ph -> ta ) ) ) )
4 3 com4r 
 |-  ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )