Theorem a1ddd

Description: Triple deduction introducing an antecedent to a wff. Deduction associated with a1dd . Double deduction associated with a1d . Triple deduction associated with ax-1 and a1i . (Contributed by Jeff Hankins, 4-Aug-2009)

	Ref	Expression
Hypothesis	a1ddd.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \tau \right)\right)$$
Assertion	a1ddd	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		a1ddd.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \tau \right)\right)$$
2		ax-1	$$⊢\tau \to \left(\theta \to \tau \right)$$
3	1 2	syl8	$$⊢\phi \to \left(\psi \to \left(\chi \to \left(\theta \to \tau \right)\right)\right)$$