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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
StepHypRef Expression
1 biimt 325 . 2  |-  ( -. 
ph  ->  ( -.  ps  <->  ( -.  ph  ->  -.  ps ) ) )
2 con34b 283 . 2  |-  ( ( ps  ->  ph )  <->  ( -.  ph 
->  -.  ps ) )
31, 2syl6bbr 254 1  |-  ( -. 
ph  ->  ( -.  ps  <->  ( ps  ->  ph ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176
This theorem is referenced by:  fnsuppres  5748  axpownd  8239  largei  22863
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177
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