Theorem mp3anl1

Description: An inference based on modus ponens. (Contributed by NM, 24-Feb-2005)

	Ref	Expression
Hypotheses	mp3anl1.1	$$⊢\phi$$
	mp3anl1.2	$$⊢\left(\left(\phi \wedge \psi \wedge \chi \right)\wedge \theta \right)\to \tau$$
Assertion	mp3anl1	$$⊢\left(\left(\psi \wedge \chi \right)\wedge \theta \right)\to \tau$$

Proof

Step	Hyp	Ref	Expression
1		mp3anl1.1	$$⊢\phi$$
2		mp3anl1.2	$$⊢\left(\left(\phi \wedge \psi \wedge \chi \right)\wedge \theta \right)\to \tau$$
3	2	ex	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \left(\theta \to \tau \right)$$
4	1 3	mp3an1	$$⊢\left(\psi \wedge \chi \right)\to \left(\theta \to \tau \right)$$
5	4	imp	$$⊢\left(\left(\psi \wedge \chi \right)\wedge \theta \right)\to \tau$$