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 ) )