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 )