Theorem mpan2i

Description: An inference based on modus ponens. (Contributed by NM, 10-Apr-1994) (Proof shortened by Wolf Lammen, 19-Nov-2012)

	Ref	Expression
Hypotheses	mpan2i.1	$$⊢\chi$$
	mpan2i.2	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$
Assertion	mpan2i	$$⊢\phi \to \left(\psi \to \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		mpan2i.1	$$⊢\chi$$
2		mpan2i.2	$$⊢\phi \to \left(\left(\psi \wedge \chi \right)\to \theta \right)$$
3	1	a1i	$$⊢\phi \to \chi$$
4	3 2	mpan2d	$$⊢\phi \to \left(\psi \to \theta \right)$$