Metamath Proof Explorer


Theorem 3impib

Description: Importation to triple conjunction. (Contributed by NM, 13-Jun-2006)

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

Proof

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