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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