Theorem syl5ibrcom

Description: A mixed syllogism inference. (Contributed by NM, 20-Jun-2007)

	Ref	Expression
Hypotheses	syl5ibr.1	⊢ ( 𝜑 → 𝜃 )
	syl5ibr.2	⊢ ( 𝜒 → ( 𝜓 ↔ 𝜃 ) )
Assertion	syl5ibrcom	⊢ ( 𝜑 → ( 𝜒 → 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		syl5ibr.1	⊢ ( 𝜑 → 𝜃 )
2		syl5ibr.2	⊢ ( 𝜒 → ( 𝜓 ↔ 𝜃 ) )
3	1 2	syl5ibr	⊢ ( 𝜒 → ( 𝜑 → 𝜓 ) )
4	3	com12	⊢ ( 𝜑 → ( 𝜒 → 𝜓 ) )