Theorem a1dd

Description: Double deduction introducing an antecedent. Deduction associated with a1d . Double deduction associated with ax-1 and a1i . (Contributed by NM, 17-Dec-2004) (Proof shortened by Mel L. O'Cat, 15-Jan-2008)

	Ref	Expression
Hypothesis	a1dd.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	a1dd	$$⊢\phi \to \left(\psi \to \left(\theta \to \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		a1dd.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		ax-1	$$⊢\chi \to \left(\theta \to \chi \right)$$
3	1 2	syl6	$$⊢\phi \to \left(\psi \to \left(\theta \to \chi \right)\right)$$