Theorem mpan

Description: An inference based on modus ponens. (Contributed by NM, 30-Aug-1993) (Proof shortened by Wolf Lammen, 7-Apr-2013)

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

Proof

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