Theorem grpmgmd

Description: A group is a magma, deduction form. (Contributed by SN, 14-Apr-2025)

	Ref	Expression
Hypothesis	grpmgmd.g	⊢ ( 𝜑 → 𝐺 ∈ Grp )
Assertion	grpmgmd	⊢ ( 𝜑 → 𝐺 ∈ Mgm )

Proof

Step	Hyp	Ref	Expression
1		grpmgmd.g	⊢ ( 𝜑 → 𝐺 ∈ Grp )
2	1	grpmndd	⊢ ( 𝜑 → 𝐺 ∈ Mnd )
3		mndmgm	⊢ ( 𝐺 ∈ Mnd → 𝐺 ∈ Mgm )
4	2 3	syl	⊢ ( 𝜑 → 𝐺 ∈ Mgm )