Theorem mp3anr1

Description: An inference based on modus ponens. (Contributed by NM, 4-Nov-2006)

	Ref	Expression
Hypotheses	mp3anr1.1	$$⊢\psi$$
	mp3anr1.2	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \wedge \theta \right)\right)\to \tau$$
Assertion	mp3anr1	$$⊢\left(\phi \wedge \left(\chi \wedge \theta \right)\right)\to \tau$$

Proof

Step	Hyp	Ref	Expression
1		mp3anr1.1	$$⊢\psi$$
2		mp3anr1.2	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \wedge \theta \right)\right)\to \tau$$
3	2	ancoms	$$⊢\left(\left(\psi \wedge \chi \wedge \theta \right)\wedge \phi \right)\to \tau$$
4	1 3	mp3anl1	$$⊢\left(\left(\chi \wedge \theta \right)\wedge \phi \right)\to \tau$$
5	4	ancoms	$$⊢\left(\phi \wedge \left(\chi \wedge \theta \right)\right)\to \tau$$