Theorem mtt 329

Description: Modus-tollens-like theorem. (Contributed by NM, 7-Apr-2001.) (Proof shortened by Wolf Lammen, 12-Nov-2012.)

Assertion

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

Proof of Theorem mtt

Step	Hyp	Ref	Expression
1		biimt 325	. 2 |- (-. ph -> (-. ps <-> (-. ph -> -. ps)))
2		con34b 283	. 2 |- ((ps -> ph) <-> (-. ph -> -. ps))
3	1, 2	syl6bbr 254	1 |- (-. ph -> (-. 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)