Theorem sylibd

Description: A syllogism deduction. (Contributed by NM, 3-Aug-1994)

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

Proof

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