Theorem syl6d

Description: A nested syllogism deduction. Deduction associated with syl6 . (Contributed by NM, 11-May-1993) (Proof shortened by Josh Purinton, 29-Dec-2000) (Proof shortened by Mel L. O'Cat, 2-Feb-2006)

	Ref	Expression
Hypotheses	syl6d.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
	syl6d.2	$$⊢\phi \to \left(\theta \to \tau \right)$$
Assertion	syl6d	$$⊢\phi \to \left(\psi \to \left(\chi \to \tau \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		syl6d.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
2		syl6d.2	$$⊢\phi \to \left(\theta \to \tau \right)$$
3	2	a1d	$$⊢\phi \to \left(\psi \to \left(\theta \to \tau \right)\right)$$
4	1 3	syldd	$$⊢\phi \to \left(\psi \to \left(\chi \to \tau \right)\right)$$