Theorem expl 378

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 364	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	impd 254	1 |- ( ph -> ( ( ps /\ ch ) -> th ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is used by:  domssr  7070  ssenen  7158  recclnq  7765  shftfvalg  11604  shftfval  11607  fsum2dlemstep  12225  fprod2dlemstep  12413  prmpwdvds  13162  quscrng  14978  tgtop  15311