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Metamath Proof Explorer

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 )