Theorem impl 372

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

Hypothesis

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

Assertion

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

Proof of Theorem impl

Step	Hyp	Ref	Expression
1		impl.1	. . 3 |- ( ph -> ( ( ps /\ ch ) -> th ) )
2	1	expd 254	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	imp31 252	1 |- ( ( ( ph /\ ps ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem is referenced by:  sbc2iedv  2886  csbie2t  2950  foco2  5339  erth  6173  distrlem1prl  6772  distrlem1pru  6773  uz11  8641  divgcdcoprm0  10483  cncongr1  10485