Theorem mpanl1

Description: An inference based on modus ponens. (Contributed by NM, 16-Aug-1994) (Proof shortened by Wolf Lammen, 7-Apr-2013)

	Ref	Expression
Hypotheses	mpanl1.1	$$⊢\phi$$
	mpanl1.2	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
Assertion	mpanl1	$$⊢\left(\psi \wedge \chi \right)\to \theta$$

Proof

Step	Hyp	Ref	Expression
1		mpanl1.1	$$⊢\phi$$
2		mpanl1.2	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\to \theta$$
3	1	jctl	$$⊢\psi \to \left(\phi \wedge \psi \right)$$
4	3 2	sylan	$$⊢\left(\psi \wedge \chi \right)\to \theta$$