Theorem mp3an

Description: An inference based on modus ponens. (Contributed by NM, 14-May-1999)

	Ref	Expression
Hypotheses	mp3an.1	$$⊢\phi$$
	mp3an.2	$$⊢\psi$$
	mp3an.3	$$⊢\chi$$
	mp3an.4	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
Assertion	mp3an	$$⊢\theta$$

Proof

Step	Hyp	Ref	Expression
1		mp3an.1	$$⊢\phi$$
2		mp3an.2	$$⊢\psi$$
3		mp3an.3	$$⊢\chi$$
4		mp3an.4	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
5	1 4	mp3an1	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
6	2 3 5	mp2an	$$⊢\theta$$