Theorem mpanr12

Description: An inference based on modus ponens. (Contributed by NM, 24-Jul-2009)

	Ref	Expression
Hypotheses	mpanr12.1	$$⊢\psi$$
	mpanr12.2	$$⊢\chi$$
	mpanr12.3	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \right)\right)\to \theta$$
Assertion	mpanr12	$$⊢\phi \to \theta$$

Proof

Step	Hyp	Ref	Expression
1		mpanr12.1	$$⊢\psi$$
2		mpanr12.2	$$⊢\chi$$
3		mpanr12.3	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \right)\right)\to \theta$$
4	1 3	mpanr1	$$⊢\left(\phi \wedge \chi \right)\to \theta$$
5	2 4	mpan2	$$⊢\phi \to \theta$$