Theorem mp3an2i

Description: mp3an with antecedents in standard conjunction form and with two hypotheses which are implications. (Contributed by Alan Sare, 28-Aug-2016)

	Ref	Expression
Hypotheses	mp3an2i.1	$$⊢\phi$$
	mp3an2i.2	$$⊢\psi \to \chi$$
	mp3an2i.3	$$⊢\psi \to \theta$$
	mp3an2i.4	$$⊢\left(\phi \wedge \chi \wedge \theta \right)\to \tau$$
Assertion	mp3an2i	$$⊢\psi \to \tau$$

Proof

Step	Hyp	Ref	Expression
1		mp3an2i.1	$$⊢\phi$$
2		mp3an2i.2	$$⊢\psi \to \chi$$
3		mp3an2i.3	$$⊢\psi \to \theta$$
4		mp3an2i.4	$$⊢\left(\phi \wedge \chi \wedge \theta \right)\to \tau$$
5	1 4	mp3an1	$$⊢\left(\chi \wedge \theta \right)\to \tau$$
6	2 3 5	syl2anc	$$⊢\psi \to \tau$$