Theorem lmodgrpd

Description: A left module is a group. (Contributed by SN, 16-May-2024)

	Ref	Expression
Hypothesis	lmodgrpd.1	$$⊢\phi \to W\in \mathrm{LMod}$$
Assertion	lmodgrpd	$$⊢\phi \to W\in \mathrm{Grp}$$

Proof

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