Metamath Proof Explorer


Theorem 3imp2

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

Ref Expression
Hypothesis 3imp1.1
|- ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
Assertion 3imp2
|- ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )

Proof

Step Hyp Ref Expression
1 3imp1.1
 |-  ( ph -> ( ps -> ( ch -> ( th -> ta ) ) ) )
2 1 3impd
 |-  ( ph -> ( ( ps /\ ch /\ th ) -> ta ) )
3 2 imp
 |-  ( ( ph /\ ( ps /\ ch /\ th ) ) -> ta )