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 )

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:  sbc2iedv  3124  csbie2t  3196  foco2  5959  erth  6853  distrlem1prl  7949  distrlem1pru  7950  uz11  9945  elpq  10049  divgcdcoprm0  12879  cncongr1  12881  prmpwdvds  13134  ballotfilemimin  13249  issgrpd  13727  dfgrp3mlem  13903  efltlemlt  15875  clwwlkext2edg  16663