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Theorem mt2bi 674
Description: A false consequent falsifies an antecedent. (Contributed by NM, 19-Aug-1993.) (Proof shortened by Wolf Lammen, 12-Nov-2012.)
Hypothesis
Ref Expression
mt2bi.1  |-  ph
Assertion
Ref Expression
mt2bi  |-  ( -. 
ps 
<->  ( ps  ->  -.  ph ) )

Proof of Theorem mt2bi
StepHypRef Expression
1 mt2bi.1 . . 3  |-  ph
21a1bi 242 . 2  |-  ( -. 
ps 
<->  ( ph  ->  -.  ps ) )
3 con2b 659 . 2  |-  ( (
ph  ->  -.  ps )  <->  ( ps  ->  -.  ph )
)
42, 3bitri 183 1  |-  ( -. 
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: (None)
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