Theorem syl5ibr

Description: A mixed syllogism inference. (Contributed by NM, 3-Apr-1994)

	Ref	Expression
Hypotheses	syl5ibr.1	⊢ ( 𝜑 → 𝜃 )
	syl5ibr.2	⊢ ( 𝜒 → ( 𝜓 ↔ 𝜃 ) )
Assertion	syl5ibr	⊢ ( 𝜒 → ( 𝜑 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		syl5ibr.1	⊢ ( 𝜑 → 𝜃 )
2		syl5ibr.2	⊢ ( 𝜒 → ( 𝜓 ↔ 𝜃 ) )
3	2	bicomd	⊢ ( 𝜒 → ( 𝜃 ↔ 𝜓 ) )
4	1 3	syl5ib	⊢ ( 𝜒 → ( 𝜑 → 𝜓 ) )