Theorem mpanr1

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

	Ref	Expression
Hypotheses	mpanr1.1	$$⊢\psi$$
	mpanr1.2	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \right)\right)\to \theta$$
Assertion	mpanr1	$$⊢\left(\phi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		mpanr1.1	$$⊢\psi$$
2		mpanr1.2	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \right)\right)\to \theta$$
3	2	anassrs	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
4	1 3	mpanl2	$$⊢\left(\phi \wedge \chi \right)\to \theta$$