Theorem sylnib

Description: A mixed syllogism inference from an implication and a biconditional. (Contributed by Wolf Lammen, 16-Dec-2013)

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

Proof

Step	Hyp	Ref	Expression
1		sylnib.1	⊢ ( 𝜑 → ¬ 𝜓 )
2		sylnib.2	⊢ ( 𝜓 ↔ 𝜒 )
3	2	biimpri	⊢ ( 𝜒 → 𝜓 )
4	1 3	nsyl	⊢ ( 𝜑 → ¬ 𝜒 )