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Metamath Proof Explorer

Theorem mt2bi

Description: A false consequent falsifies an antecedent. (Contributed by NM, 19-Aug-1993) (Proof shortened by Wolf Lammen, 12-Nov-2012)

Ref Expression
Hypothesis mt2bi.1 
|- ph
Assertion mt2bi 
|- ( -. ps <-> ( ps -> -. ph ) )

Proof

Step Hyp Ref Expression
1 mt2bi.1 
 |-  ph
2 1 a1bi 
 |-  ( -. ps <-> ( ph -> -. ps ) )
3 con2b 
 |-  ( ( ph -> -. ps ) <-> ( ps -> -. ph ) )
4 2 3 bitri 
 |-  ( -. ps <-> ( ps -> -. ph ) )