Metamath Proof Explorer


Theorem mt2d

Description: Modus tollens deduction. (Contributed by NM, 4-Jul-1994)

Ref Expression
Hypotheses mt2d.1 φ χ
mt2d.2 φ ψ ¬ χ
Assertion mt2d φ ¬ ψ

Proof

Step Hyp Ref Expression
1 mt2d.1 φ χ
2 mt2d.2 φ ψ ¬ χ
3 2 con2d φ χ ¬ ψ
4 1 3 mpd φ ¬ ψ