Theorem con3and 428

Description: Variant of con3d 125 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 125	. 2 |- (ph -> (-. ch -> -. ps))
3	2	imp 418	1 |- ((ph /\ -. ch) -> -. ps)

Syntax hints:  -. wn 3   -> wi 4   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  ax12olem1  1927  nelneq  2451  nelneq2  2452