Theorem mpanlr1

Description: An inference based on modus ponens. (Contributed by NM, 30-Dec-2004) (Proof shortened by Wolf Lammen, 7-Apr-2013)

	Ref	Expression
Hypotheses	mpanlr1.1	$$⊢\psi$$
	mpanlr1.2	$$⊢\left(\left(\phi \wedge \left(\psi \wedge \chi \right)\right)\wedge \theta \right)\to \tau$$
Assertion	mpanlr1	$$⊢\left(\left(\phi \wedge \chi \right)\wedge \theta \right)\to \tau$$

Proof

Step	Hyp	Ref	Expression
1		mpanlr1.1	$$⊢\psi$$
2		mpanlr1.2	$$⊢\left(\left(\phi \wedge \left(\psi \wedge \chi \right)\right)\wedge \theta \right)\to \tau$$
3	1	jctl	$$⊢\chi \to \left(\psi \wedge \chi \right)$$
4	3 2	sylanl2	$$⊢\left(\left(\phi \wedge \chi \right)\wedge \theta \right)\to \tau$$