Theorem lvecgrp

Description: A vector space is a group. (Contributed by SN, 28-May-2023)

	Ref	Expression
Assertion	lvecgrp	$$⊢W\in \mathrm{LVec}\to W\in \mathrm{Grp}$$

Proof

Step	Hyp	Ref	Expression
1		lveclmod	$$⊢W\in \mathrm{LVec}\to W\in \mathrm{LMod}$$
2		lmodgrp	$$⊢W\in \mathrm{LMod}\to W\in \mathrm{Grp}$$
3	1 2	syl	$$⊢W\in \mathrm{LVec}\to W\in \mathrm{Grp}$$