Theorem sylbird

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

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

Proof

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