Theorem con3dimp 636

Description: Variant of con3d 632 with importation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)

Hypothesis

Ref	Expression
con3dimp.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
con3dimp	|- ( ( ph /\ -. ch ) -> -. ps )

Proof of Theorem con3dimp

Step	Hyp	Ref	Expression
1		con3dimp.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	con3d 632	. 2 |- ( ph -> ( -. ch -> -. ps ) )
3	2	imp 124	1 |- ( ( ph /\ -. ch ) -> -. ps )

Syntax hints:   -. wn 3   -> 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-in1 615  ax-in2 616

This theorem is referenced by:  stoic1a  1447  nelneq  2307  nelneq2  2308  nelss  3258  nnnninf  7243  bcpasc  10933  fiinfnf1o  10953  nnoddn2prmb  12660  pcprod  12744  lgsdir  15587  2lgslem2  15644  2lgs  15656  pw1nct  16081