Theorem con3dimp 630

Description: Variant of con3d 626 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 626	. 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 609  ax-in2 610

This theorem is referenced by:  nelneq  2271  nelneq2  2272  nelss  3208  nnnninf  7098  bcpasc  10687  fiinfnf1o  10707  nnoddn2prmb  12203  pcprod  12285  lgsdir  13689  pw1nct  13996