Theorem sylsyld

Description: A double syllogism inference. (Contributed by Alan Sare, 20-Apr-2011)

	Ref	Expression
Hypotheses	sylsyld.1	$$⊢\phi \to \psi$$
	sylsyld.2	$$⊢\phi \to \left(\chi \to \theta \right)$$
	sylsyld.3	$$⊢\psi \to \left(\theta \to \tau \right)$$
Assertion	sylsyld	$$⊢\phi \to \left(\chi \to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		sylsyld.1	$$⊢\phi \to \psi$$
2		sylsyld.2	$$⊢\phi \to \left(\chi \to \theta \right)$$
3		sylsyld.3	$$⊢\psi \to \left(\theta \to \tau \right)$$
4	1 3	syl	$$⊢\phi \to \left(\theta \to \tau \right)$$
5	2 4	syld	$$⊢\phi \to \left(\chi \to \tau \right)$$