Metamath Proof Explorer


Theorem imp31

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

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

Proof

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