Theorem impl 380

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 258	. 2 |- ( ph -> ( ps -> ( ch -> th ) ) )
3	2	imp31 256	1 |- ( ( ( ph /\ ps ) /\ ch ) -> th )

Syntax hints:   -> wi 4   /\ wa 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem is referenced by:  sbc2iedv  3058  csbie2t  3129  foco2  5796  erth  6633  distrlem1prl  7642  distrlem1pru  7643  uz11  9615  elpq  9714  divgcdcoprm0  12239  cncongr1  12241  prmpwdvds  12493  issgrpd  12995  dfgrp3mlem  13170  efltlemlt  14909