Theorem mt2bi 535

Description: A false consequent falsifies an antecedent.

Hypothesis

Ref	Expression
mt2bi.1	|- ph

Assertion

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

Proof of Theorem mt2bi

Step	Hyp	Ref	Expression
1		pm2.21 71	. 2 |- (-. ps -> (ps -> -. ph))
2		mt2bi.1	. . 3 |- ph
3		con2 82	. . 3 |- ((ps -> -. ph) -> (ph -> -. ps))
4	2, 3	mpi 44	. 2 |- ((ps -> -. ph) -> -. ps)
5	1, 4	impbi 139	1 |- (-. ps <-> (ps -> -. ph))

Syntax hints:  -. wn 1   -> wi 2   <-> wb 127

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128

metamath.org