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Metamath Proof Explorer

Theorem lmhmghmd

Description: A module homomorphism is a group homomorphism. (Contributed by Thierry Arnoux, 2-Apr-2025)

		Ref	Expression
	Hypothesis	lmhmghmd.1	$⊢ φ \to F \in (S LMHom T)$
	Assertion	lmhmghmd	$⊢ φ \to F \in (S GrpHom T)$

Step	Hyp	Ref	Expression
1		lmhmghmd.1	$⊢ φ \to F \in (S LMHom T)$
2		lmghm	$⊢ F \in (S LMHom T) \to F \in (S GrpHom T)$
3	1 2	syl	$⊢ φ \to F \in (S GrpHom T)$