This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem nlmngp2

Description: The scalar component of a left module is a normed group. (Contributed by Mario Carneiro, 4-Oct-2015)

		Ref	Expression
	Hypothesis	nlmnrg.1	$⊢ F = Scalar (W)$
	Assertion	nlmngp2	$⊢ W \in NrmMod \to F \in NrmGrp$

Step	Hyp	Ref	Expression
1		nlmnrg.1	$⊢ F = Scalar (W)$
2	1	nlmnrg	$⊢ W \in NrmMod \to F \in NrmRing$
3		nrgngp	$⊢ F \in NrmRing \to F \in NrmGrp$
4	2 3	syl	$⊢ W \in NrmMod \to F \in NrmGrp$