Theorem mpanl2

Description: An inference based on modus ponens. (Contributed by NM, 16-Aug-1994) (Proof shortened by Andrew Salmon, 7-May-2011)

	Ref	Expression
Hypotheses	mpanl2.1	$$⊢\psi$$
	mpanl2.2	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
Assertion	mpanl2	$$⊢\left(\phi \wedge \chi \right)\to \theta$$

Proof

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