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 ) ) )