Theorem a2d

Description: Deduction distributing an embedded antecedent. Deduction form of ax-2 . (Contributed by NM, 23-Jun-1994)

	Ref	Expression
Hypothesis	a2d.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
Assertion	a2d	$$⊢\phi \to \left(\left(\psi \to \chi \right)\to \left(\psi \to \theta \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		a2d.1	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
2		ax-2	$$⊢\left(\psi \to \left(\chi \to \theta \right)\right)\to \left(\left(\psi \to \chi \right)\to \left(\psi \to \theta \right)\right)$$
3	1 2	syl	$$⊢\phi \to \left(\left(\psi \to \chi \right)\to \left(\psi \to \theta \right)\right)$$