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Theorem mtt 675
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
StepHypRef Expression
1 pm2.21 607 . 2  |-  ( -. 
ps  ->  ( ps  ->  ph ) )
2 con3 632 . . 3  |-  ( ( ps  ->  ph )  -> 
( -.  ph  ->  -. 
ps ) )
32com12 30 . 2  |-  ( -. 
ph  ->  ( ( ps 
->  ph )  ->  -.  ps ) )
41, 3impbid2 142 1  |-  ( -. 
ph  ->  ( -.  ps  <->  ( ps  ->  ph ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  nbn2  687  dfnot  1350
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