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Metamath Proof Explorer

Theorem mt3d

Description: Modus tollens deduction. (Contributed by NM, 26-Mar-1995)

Ref Expression
Hypotheses mt3d.1 ⊢ φ → ¬ χ
mt3d.2 ⊢ φ → ¬ ψ → χ
Assertion mt3d ⊢ φ → ψ

Proof

Step Hyp Ref Expression
1 mt3d.1 ⊢ φ → ¬ χ
2 mt3d.2 ⊢ φ → ¬ ψ → χ
3 2 con1d ⊢ φ → ¬ χ → ψ
4 1 3 mpd ⊢ φ → ψ