Theorem mp3an2ani

Description: An elimination deduction. (Contributed by Alan Sare, 17-Oct-2017)

	Ref	Expression
Hypotheses	mp3an2ani.1	$$⊢\phi$$
	mp3an2ani.2	$$⊢\psi \to \chi$$
	mp3an2ani.3	$$⊢\left(\psi \wedge \theta \right)\to \tau$$
	mp3an2ani.4	$$⊢\left(\phi \wedge \chi \wedge \tau \right)\to \eta$$
Assertion	mp3an2ani	$$⊢\left(\psi \wedge \theta \right)\to \eta$$

Proof

Step	Hyp	Ref	Expression
1		mp3an2ani.1	$$⊢\phi$$
2		mp3an2ani.2	$$⊢\psi \to \chi$$
3		mp3an2ani.3	$$⊢\left(\psi \wedge \theta \right)\to \tau$$
4		mp3an2ani.4	$$⊢\left(\phi \wedge \chi \wedge \tau \right)\to \eta$$
5	1 2 3 4	mp3an3an	$$⊢\left(\psi \wedge \left(\psi \wedge \theta \right)\right)\to \eta$$
6	5	anabss5	$$⊢\left(\psi \wedge \theta \right)\to \eta$$