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Metamath Proof Explorer

Theorem nsyl3

Description: A negated syllogism inference. (Contributed by NM, 1-Dec-1995)

Ref Expression
Hypotheses nsyl3.1 ⊢ φ → ¬ ψ
nsyl3.2 ⊢ χ → ψ
Assertion nsyl3 ⊢ χ → ¬ φ

Proof

Step Hyp Ref Expression
1 nsyl3.1 ⊢ φ → ¬ ψ
2 nsyl3.2 ⊢ χ → ψ
3 1 a1i ⊢ χ → φ → ¬ ψ
4 2 3 mt2d ⊢ χ → ¬ φ