Theorem mt2bi 641

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 241	. 2 |- ( -. ps <-> ( ph -> -. ps ) )
3		con2b 625	. 2 |- ( ( ph -> -. ps ) <-> ( ps -> -. ph ) )
4	2, 3	bitri 182	1 |- ( -. ps <-> ( ps -> -. ph ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577

This theorem depends on definitions:  df-bi 115

This theorem is referenced by: (None)