Theorem mpdd

Description: A nested modus ponens deduction. Double deduction associated with ax-mp . Deduction associated with mpd . (Contributed by NM, 12-Dec-2004)

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

Proof

Step	Hyp	Ref	Expression
1		mpdd.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		mpdd.2	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
3	2	a2d	$$⊢\phi \to \left(\left(\psi \to \chi \right)\to \left(\psi \to \theta \right)\right)$$
4	1 3	mpd	$$⊢\phi \to \left(\psi \to \theta \right)$$