Theorem syl5ibcom

Description: A mixed syllogism inference. (Contributed by NM, 19-Jun-2007)

	Ref	Expression
Hypotheses	syl5ib.1	⊢ ( 𝜑 → 𝜓 )
	syl5ib.2	⊢ ( 𝜒 → ( 𝜓 ↔ 𝜃 ) )
Assertion	syl5ibcom	⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		syl5ib.1	⊢ ( 𝜑 → 𝜓 )
2		syl5ib.2	⊢ ( 𝜒 → ( 𝜓 ↔ 𝜃 ) )
3	1 2	syl5ib	⊢ ( 𝜒 → ( 𝜑 → 𝜃 ) )
4	3	com12	⊢ ( 𝜑 → ( 𝜒 → 𝜃 ) )