Theorem nsyl5

Description: A negated syllogism inference. (Contributed by Wolf Lammen, 20-May-2024)

	Ref	Expression
Hypotheses	nsyl4.1	⊢ ( 𝜑 → 𝜓 )
	nsyl4.2	⊢ ( ¬ 𝜑 → 𝜒 )
Assertion	nsyl5	⊢ ( ¬ 𝜓 → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		nsyl4.1	⊢ ( 𝜑 → 𝜓 )
2		nsyl4.2	⊢ ( ¬ 𝜑 → 𝜒 )
3	1 2	nsyl4	⊢ ( ¬ 𝜒 → 𝜓 )
4	3	con1i	⊢ ( ¬ 𝜓 → 𝜒 )