Theorem sylbird

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

	Ref	Expression
Hypotheses	sylbird.1	$$⊢\phi \to \left(\chi \leftrightarrow \psi \right)$$
	sylbird.2	$$⊢\phi \to \left(\chi \to \theta \right)$$
Assertion	sylbird	$$⊢\phi \to \left(\psi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		sylbird.1	$$⊢\phi \to \left(\chi \leftrightarrow \psi \right)$$
2		sylbird.2	$$⊢\phi \to \left(\chi \to \theta \right)$$
3	1	biimprd	$$⊢\phi \to \left(\psi \to \chi \right)$$
4	3 2	syld	$$⊢\phi \to \left(\psi \to \theta \right)$$