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Theorem mtt 643
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 pm2.21 580 . 2  |-  ( -. 
ps  ->  ( ps  ->  ph ) )
2 con3 604 . . 3  |-  ( ( ps  ->  ph )  -> 
( -.  ph  ->  -. 
ps ) )
32com12 30 . 2  |-  ( -. 
ph  ->  ( ( ps 
->  ph )  ->  -.  ps ) )
41, 3impbid2 141 1  |-  ( -. 
ph  ->  ( -.  ps  <->  ( ps  ->  ph ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  nbn2  646  dfnot  1303
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