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Metamath Proof Explorer

Theorem nsyld

Description: A negated syllogism deduction. (Contributed by NM, 9-Apr-2005)

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

Proof

Step Hyp Ref Expression
1 nsyld.1 ⊢ φ → ψ → ¬ χ
2 nsyld.2 ⊢ φ → τ → χ
3 2 con3d ⊢ φ → ¬ χ → ¬ τ
4 1 3 syld ⊢ φ → ψ → ¬ τ