Theorem lmhmghmd

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

	Ref	Expression
Hypothesis	lmhmghmd.1	|- ( ph -> F e. ( S LMHom T ) )
Assertion	lmhmghmd	|- ( ph -> F e. ( S GrpHom T ) )

Proof

Step	Hyp	Ref	Expression
1		lmhmghmd.1	|- ( ph -> F e. ( S LMHom T ) )
2		lmghm	|- ( F e. ( S LMHom T ) -> F e. ( S GrpHom T ) )
3	1 2	syl	|- ( ph -> F e. ( S GrpHom T ) )