Theorem con3dimp 625

Description: Variant of con3d 621 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 621	. 2 |- ( ph -> ( -. ch -> -. ps ) )
3	2	imp 123	1 |- ( ( ph /\ -. ch ) -> -. ps )

Syntax hints:   -. wn 3   -> 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-in1 604  ax-in2 605

This theorem is referenced by:  nelneq  2267  nelneq2  2268  nelss  3203  nnnninf  7090  bcpasc  10679  fiinfnf1o  10699  nnoddn2prmb  12194  pcprod  12276  lgsdir  13576  pw1nct  13883