Theorem mt2bi 328

Description: A false consequent falsifies an antecedent. (Contributed by NM, 19-Aug-1993.) (Proof shortened by Wolf Lammen, 12-Nov-2012.)

Hypothesis

Ref	Expression
mt2bi.1	|- ph

Assertion

Ref	Expression
mt2bi	|- (-. ps <-> (ps -> -. ph))

Proof of Theorem mt2bi

Step	Hyp	Ref	Expression
1		mt2bi.1	. . 3 |- ph
2	1	a1bi 327	. 2 |- (-. ps <-> (ph -> -. ps))
3		con2b 324	. 2 |- ((ph -> -. ps) <-> (ps -> -. ph))
4	2, 3	bitri 240	1 |- (-. ps <-> (ps -> -. ph))

Syntax hints:  -. wn 3   -> wi 4   <-> wb 176

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

This theorem is referenced by: (None)