Theorem mpan2

Description: An inference based on modus ponens. (Contributed by NM, 16-Sep-1993) (Proof shortened by Wolf Lammen, 19-Nov-2012)

	Ref	Expression
Hypotheses	mpan2.1	$$⊢\psi$$
	mpan2.2	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
Assertion	mpan2	$$⊢\phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		mpan2.1	$$⊢\psi$$
2		mpan2.2	$$⊢\left(\phi \wedge \psi \right)\to \chi$$
3	1	a1i	$$⊢\phi \to \psi$$
4	3 2	mpdan	$$⊢\phi \to \chi$$