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Metamath Proof Explorer

Theorem nsyli

Description: A negated syllogism inference. (Contributed by NM, 3-May-1994)

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

Proof

Step Hyp Ref Expression
1 nsyli.1 ⊢ φ → ψ → χ
2 nsyli.2 ⊢ θ → ¬ χ
3 1 con3d ⊢ φ → ¬ χ → ¬ ψ
4 2 3 syl5 ⊢ φ → θ → ¬ ψ