Theorem syl5d

Description: A nested syllogism deduction. Deduction associated with syl5 . (Contributed by NM, 14-May-1993) (Proof shortened by Josh Purinton, 29-Dec-2000) (Proof shortened by Mel L. O'Cat, 2-Feb-2006)

	Ref	Expression
Hypotheses	syl5d.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	syl5d.2	$$⊢\phi \to \left(\theta \to \left(\chi \to \tau \right)\right)$$
Assertion	syl5d	$$⊢\phi \to \left(\theta \to \left(\psi \to \tau \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		syl5d.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		syl5d.2	$$⊢\phi \to \left(\theta \to \left(\chi \to \tau \right)\right)$$
3	1	a1d	$$⊢\phi \to \left(\theta \to \left(\psi \to \chi \right)\right)$$
4	3 2	syldd	$$⊢\phi \to \left(\theta \to \left(\psi \to \tau \right)\right)$$