Theorem sylbid

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

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

Proof

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