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 ¬φ¬ψψφ

Proof

Step Hyp Ref Expression
1 biimt ¬φ¬ψ¬φ¬ψ
2 con34b ψφ¬φ¬ψ
3 1 2 bitr4di ¬φ¬ψψφ