Metamath Proof Explorer


Theorem imp32

Description: An importation inference. (Contributed by NM, 26-Apr-1994)

Ref Expression
Hypothesis imp31.1
|- ( ph -> ( ps -> ( ch -> th ) ) )
Assertion imp32
|- ( ( ph /\ ( ps /\ ch ) ) -> th )

Proof

Step Hyp Ref Expression
1 imp31.1
 |-  ( ph -> ( ps -> ( ch -> th ) ) )
2 1 impd
 |-  ( ph -> ( ( ps /\ ch ) -> th ) )
3 2 imp
 |-  ( ( ph /\ ( ps /\ ch ) ) -> th )