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Theorem mt2bi 642
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 241 . 2  |-  ( -. 
ps 
<->  ( ph  ->  -.  ps ) )
3 con2b 626 . 2  |-  ( (
ph  ->  -.  ps )  <->  ( ps  ->  -.  ph )
)
42, 3bitri 182 1  |-  ( -. 
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: (None)
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