Theorem mpdi

Description: A nested modus ponens deduction. (Contributed by NM, 16-Apr-2005) (Proof shortened by Mel L. O'Cat, 15-Jan-2008)

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

Proof

Step	Hyp	Ref	Expression
1		mpdi.1	$$⊢\psi \to \chi$$
2		mpdi.2	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
3	1	a1i	$$⊢\phi \to \left(\psi \to \chi \right)$$
4	3 2	mpdd	$$⊢\phi \to \left(\psi \to \theta \right)$$