Theorem mp3an12

Description: An inference based on modus ponens. (Contributed by NM, 13-Jul-2005)

	Ref	Expression
Hypotheses	mp3an12.1	$$⊢\phi$$
	mp3an12.2	$$⊢\psi$$
	mp3an12.3	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
Assertion	mp3an12	$$⊢\chi \to \theta$$

Proof

Step	Hyp	Ref	Expression
1		mp3an12.1	$$⊢\phi$$
2		mp3an12.2	$$⊢\psi$$
3		mp3an12.3	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \theta$$
4	1 3	mp3an1	$$⊢\left(\psi \wedge \chi \right)\to \theta$$
5	2 4	mpan	$$⊢\chi \to \theta$$