Theorem nsyl

Description: A negated syllogism inference. (Contributed by NM, 31-Dec-1993) (Proof shortened by Wolf Lammen, 2-Mar-2013)

	Ref	Expression
Hypotheses	nsyl.1	⊢ ( 𝜑 → ¬ 𝜓 )
	nsyl.2	⊢ ( 𝜒 → 𝜓 )
Assertion	nsyl	⊢ ( 𝜑 → ¬ 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		nsyl.1	⊢ ( 𝜑 → ¬ 𝜓 )
2		nsyl.2	⊢ ( 𝜒 → 𝜓 )
3	1 2	nsyl3	⊢ ( 𝜒 → ¬ 𝜑 )
4	3	con2i	⊢ ( 𝜑 → ¬ 𝜒 )