Metamath Proof Explorer

Theorem expl

Description: Export a wff from a left conjunct. (Contributed by Jeff Hankins, 28-Aug-2009)

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

Proof

Step Hyp Ref Expression
1 expl.1 
 |-  ( ( ( ph /\ ps ) /\ ch ) -> th )
2 1 exp31 
 |-  ( ph -> ( ps -> ( ch -> th ) ) )
3 2 impd 
 |-  ( ph -> ( ( ps /\ ch ) -> th ) )