Theorem mp3an2

Description: An inference based on modus ponens. (Contributed by NM, 21-Nov-1994)

	Ref	Expression
Hypotheses	mp3an2.1	$$⊢\psi$$
	mp3an2.2	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
Assertion	mp3an2	$$⊢\left(\phi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		mp3an2.1	$$⊢\psi$$
2		mp3an2.2	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
3	2	3expa	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
4	1 3	mpanl2	$$⊢\left(\phi \wedge \chi \right)\to \theta$$