Theorem expl 373

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

Hypothesis

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

Assertion

Ref	Expression
expl	|- ( ph -> ( ( ps /\ ch ) -> th ) )

Proof of Theorem expl

Step	Hyp	Ref	Expression
1		expl.1	. . 3 |- ( ( ( ph /\ ps ) /\ ch ) -> th )
2	1	exp31 359	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	impd 252	1 |- ( ph -> ( ( ps /\ ch ) -> th ) )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem is referenced by:  ssenen  6698  recclnq  7148  shftfvalg  10483  shftfval  10486  fsum2dlemstep  11095  tgtop  12080