Theorem mp3an1

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

	Ref	Expression
Hypotheses	mp3an1.1	$$⊢\phi$$
	mp3an1.2	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
Assertion	mp3an1	$$⊢\left(\psi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		mp3an1.1	$$⊢\phi$$
2		mp3an1.2	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
3	2	3expb	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \right)\right)\to \theta$$
4	1 3	mpan	$$⊢\left(\psi \wedge \chi \right)\to \theta$$