Theorem sylbid

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

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

Proof

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