Theorem syl5ib

Description: A mixed syllogism inference. (Contributed by NM, 12-Jan-1993)

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

Proof

Step	Hyp	Ref	Expression
1		syl5ib.1	⊢ ( 𝜑 → 𝜓 )
2		syl5ib.2	⊢ ( 𝜒 → ( 𝜓 ↔ 𝜃 ) )
3	2	biimpd	⊢ ( 𝜒 → ( 𝜓 → 𝜃 ) )
4	1 3	syl5	⊢ ( 𝜒 → ( 𝜑 → 𝜃 ) )