Theorem sylibd

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

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

Proof

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