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Metamath Proof Explorer

Theorem mtt

Description: Modus-tollens-like theorem. (Contributed by NM, 7-Apr-2001) (Proof shortened by Wolf Lammen, 12-Nov-2012)

Ref Expression
Assertion mtt 
|- ( -. ph -> ( -. ps <-> ( ps -> ph ) ) )

Proof

Step Hyp Ref Expression
1 biimt 
 |-  ( -. ph -> ( -. ps <-> ( -. ph -> -. ps ) ) )
2 con34b 
 |-  ( ( ps -> ph ) <-> ( -. ph -> -. ps ) )
3 1 2 bitr4di 
 |-  ( -. ph -> ( -. ps <-> ( ps -> ph ) ) )