Metamath Proof Explorer

Theorem impl

Description: Export a wff from a left conjunct. (Contributed by Mario Carneiro, 9-Jul-2014)

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

Proof

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