Theorem mp3an1i

Description: An inference based on modus ponens. (Contributed by NM, 5-Jul-2005)

	Ref	Expression
Hypotheses	mp3an1i.1	$$⊢\psi$$
	mp3an1i.2	$$⊢\phi \to \left(\left(\psi \wedge \chi \wedge \theta \right)\to \tau \right)$$
Assertion	mp3an1i	$$⊢\phi \to \left(\left(\chi \wedge \theta \right)\to \tau \right)$$

Proof

Step	Hyp	Ref	Expression
1		mp3an1i.1	$$⊢\psi$$
2		mp3an1i.2	$$⊢\phi \to \left(\left(\psi \wedge \chi \wedge \theta \right)\to \tau \right)$$
3	2	com12	$$⊢\left(\psi \wedge \chi \wedge \theta \right)\to \left(\phi \to \tau \right)$$
4	1 3	mp3an1	$$⊢\left(\chi \wedge \theta \right)\to \left(\phi \to \tau \right)$$
5	4	com12	$$⊢\phi \to \left(\left(\chi \wedge \theta \right)\to \tau \right)$$