Theorem mp3an3an

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	mp3an3an.1	$$⊢\phi$$
	mp3an3an.2	$$⊢\psi \to \chi$$
	mp3an3an.3	$$⊢\theta \to \tau$$
	mp3an3an.4	$$⊢\left(\phi \wedge \chi \wedge \tau \right)\to \eta$$
Assertion	mp3an3an	$$⊢\left(\psi \wedge \theta \right)\to \eta$$

Proof

Step	Hyp	Ref	Expression
1		mp3an3an.1	$$⊢\phi$$
2		mp3an3an.2	$$⊢\psi \to \chi$$
3		mp3an3an.3	$$⊢\theta \to \tau$$
4		mp3an3an.4	$$⊢\left(\phi \wedge \chi \wedge \tau \right)\to \eta$$
5	1 4	mp3an1	$$⊢\left(\chi \wedge \tau \right)\to \eta$$
6	2 3 5	syl2an	$$⊢\left(\psi \wedge \theta \right)\to \eta$$