Theorem mt2bi 712

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 76	. 2 |- (-. ps -> (ps -> -. ph))
2		mt2bi.1	. . 3 |- ph
3		con2 90	. . 3 |- ((ps -> -. ph) -> (ph -> -. ps))
4	2, 3	mpi 44	. 2 |- ((ps -> -. ph) -> -. ps)
5	1, 4	impbi 157	1 |- (-. ps <-> (ps -> -. ph))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147

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