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 ¬ ψ ψ φ

Proof

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