Theorem mtt 534

Description: Modus-tollens-like theorem.

Assertion

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

Proof of Theorem mtt

Step	Hyp	Ref	Expression
1		pm2.21 71	. . 3 |- (-. ps -> (ps -> ph))
2	1	a1i 7	. 2 |- (-. ph -> (-. ps -> (ps -> ph)))
3		con3 86	. . 3 |- ((ps -> ph) -> (-. ph -> -. ps))
4	3	com12 13	. 2 |- (-. ph -> ((ps -> ph) -> -. ps))
5	2, 4	impbid 397	1 |- (-. ph -> (-. ps <-> (ps -> ph)))

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

This theorem is referenced by:  axpowndlem3 3745  axpownd 3747  large 5700

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  df-an 198

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