Theorem con3and 564

Description: Variant of con3d 561 with importation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)

Hypothesis

Ref	Expression
con3and.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
con3and	|- ( ( ph /\ -. ch ) -> -. ps )

Proof of Theorem con3and

Step	Hyp	Ref	Expression
1		con3and.1	. . 3 |- ( ph -> ( ps -> ch ) )
2	1	con3d 561	. 2 |- ( ph -> ( -. ch -> -. ps ) )
3	2	imp 115	1 |- ( ( ph /\ -. ch ) -> -. ps )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 97

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-in1 544  ax-in2 545

This theorem is referenced by:  nelneq  2138  nelneq2  2139