Metamath Proof Explorer

Theorem rrxngp

Description: Generalized Euclidean real spaces are normed groups. (Contributed by Glauco Siliprandi, 24-Dec-2020)

		Ref	Expression
	Assertion	rrxngp	$⊢ I \in V \to I \in NrmGrp$

Step	Hyp	Ref	Expression
1		eqid	$⊢ I = I$
2		eqid	$⊢ {Base}_{I} = {Base}_{I}$
3	1 2	rrxcph	$⊢ I \in V \to I \in CPreHil$
4		cphngp	$⊢ I \in CPreHil \to I \in NrmGrp$
5	3 4	syl	$⊢ I \in V \to I \in NrmGrp$