Theorem lvecgrpd

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

	Ref	Expression
Hypothesis	lvecgrpd.1	⊢ ( 𝜑 → 𝑊 ∈ LVec )
Assertion	lvecgrpd	⊢ ( 𝜑 → 𝑊 ∈ Grp )

Proof

Step	Hyp	Ref	Expression
1		lvecgrpd.1	⊢ ( 𝜑 → 𝑊 ∈ LVec )
2	1	lveclmodd	⊢ ( 𝜑 → 𝑊 ∈ LMod )
3	2	lmodgrpd	⊢ ( 𝜑 → 𝑊 ∈ Grp )