Theorem lmodgrpd

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

	Ref	Expression
Hypothesis	lmodgrpd.1	⊢ ( 𝜑 → 𝑊 ∈ LMod )
Assertion	lmodgrpd	⊢ ( 𝜑 → 𝑊 ∈ Grp )

Proof

Step	Hyp	Ref	Expression
1		lmodgrpd.1	⊢ ( 𝜑 → 𝑊 ∈ LMod )
2		lmodgrp	⊢ ( 𝑊 ∈ LMod → 𝑊 ∈ Grp )
3	1 2	syl	⊢ ( 𝜑 → 𝑊 ∈ Grp )