Theorem mp3an23

Description: An inference based on modus ponens. (Contributed by NM, 14-Jul-2005)

	Ref	Expression
Hypotheses	mp3an23.1	$$⊢\psi$$
	mp3an23.2	$$⊢\chi$$
	mp3an23.3	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
Assertion	mp3an23	$$⊢\phi \to \theta$$

Proof

Step	Hyp	Ref	Expression
1		mp3an23.1	$$⊢\psi$$
2		mp3an23.2	$$⊢\chi$$
3		mp3an23.3	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
4	2 3	mp3an3	$$⊢\left(\phi \wedge \psi \right)\to \theta$$
5	1 4	mpan2	$$⊢\phi \to \theta$$