Theorem impl 378

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 256	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	imp31 254	1 |- ( ( ( ph /\ ps ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 103

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

This theorem is referenced by:  sbc2iedv  3027  csbie2t  3097  foco2  5733  erth  6557  distrlem1prl  7544  distrlem1pru  7545  uz11  9509  elpq  9607  divgcdcoprm0  12055  cncongr1  12057  prmpwdvds  12307  efltlemlt  13489