Theorem mtt 657

Description: Modus-tollens-like theorem. (Contributed by NM, 7-Apr-2001.) (Revised by Mario Carneiro, 31-Jan-2015.)

Assertion

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

Proof of Theorem mtt

Step	Hyp	Ref	Expression
1		pm2.21 589	. 2 |- ( -. ps -> ( ps -> ph ) )
2		con3 614	. . 3 |- ( ( ps -> ph ) -> ( -. ph -> -. ps ) )
3	2	com12 30	. 2 |- ( -. ph -> ( ( ps -> ph ) -> -. ps ) )
4	1, 3	impbid2 142	1 |- ( -. ph -> ( -. ps <-> ( ps -> ph ) ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 104

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  nbn2  669  dfnot  1332