Theorem mp3an12i

Description: mp3an with antecedents in standard conjunction form and with one hypothesis an implication. (Contributed by Alan Sare, 28-Aug-2016)

	Ref	Expression
Hypotheses	mp3an12i.1	$$⊢\phi$$
	mp3an12i.2	$$⊢\psi$$
	mp3an12i.3	$$⊢\chi \to \theta$$
	mp3an12i.4	$$⊢\left(\phi \wedge \psi \wedge \theta \right)\to \tau$$
Assertion	mp3an12i	$$⊢\chi \to \tau$$

Proof

Step	Hyp	Ref	Expression
1		mp3an12i.1	$$⊢\phi$$
2		mp3an12i.2	$$⊢\psi$$
3		mp3an12i.3	$$⊢\chi \to \theta$$
4		mp3an12i.4	$$⊢\left(\phi \wedge \psi \wedge \theta \right)\to \tau$$
5	1 2 4	mp3an12	$$⊢\theta \to \tau$$
6	3 5	syl	$$⊢\chi \to \tau$$