Theorem nsyl2

Description: A negated syllogism inference. (Contributed by NM, 26-Jun-1994) (Proof shortened by Wolf Lammen, 14-Nov-2023)

	Ref	Expression
Hypotheses	nsyl2.1	⊢ ( 𝜑 → ¬ 𝜓 )
	nsyl2.2	⊢ ( ¬ 𝜒 → 𝜓 )
Assertion	nsyl2	⊢ ( 𝜑 → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		nsyl2.1	⊢ ( 𝜑 → ¬ 𝜓 )
2		nsyl2.2	⊢ ( ¬ 𝜒 → 𝜓 )
3	1 2	nsyl3	⊢ ( ¬ 𝜒 → ¬ 𝜑 )
4	3	con4i	⊢ ( 𝜑 → 𝜒 )