Theorem mpii

Description: A doubly nested modus ponens inference. (Contributed by NM, 31-Dec-1993) (Proof shortened by Wolf Lammen, 31-Jul-2012)

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

Proof

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