Theorem mpanr2

Description: An inference based on modus ponens. (Contributed by NM, 3-May-1994) (Proof shortened by Andrew Salmon, 7-May-2011) (Proof shortened by Wolf Lammen, 7-Apr-2013)

	Ref	Expression
Hypotheses	mpanr2.1	$$⊢\chi$$
	mpanr2.2	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \right)\right)\to \theta$$
Assertion	mpanr2	$$⊢\left(\phi \wedge \psi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		mpanr2.1	$$⊢\chi$$
2		mpanr2.2	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \right)\right)\to \theta$$
3	1	jctr	$$⊢\psi \to \left(\psi \wedge \chi \right)$$
4	3 2	sylan2	$$⊢\left(\phi \wedge \psi \right)\to \theta$$