Theorem mpan2d

Description: A deduction based on modus ponens. (Contributed by NM, 12-Dec-2004)

	Ref	Expression
Hypotheses	mpan2d.1	$$⊢\phi \to \chi$$
	mpan2d.2	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$
Assertion	mpan2d	$$⊢\phi \to \left(\psi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		mpan2d.1	$$⊢\phi \to \chi$$
2		mpan2d.2	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$
3	2	expd	$$⊢\phi \to \left(\psi \to \left(\chi \to \theta \right)\right)$$
4	1 3	mpid	$$⊢\phi \to \left(\psi \to \theta \right)$$