Theorem lmhmghmd

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

	Ref	Expression
Hypothesis	lmhmghmd.1	⊢ ( 𝜑 → 𝐹 ∈ ( 𝑆 LMHom 𝑇 ) )
Assertion	lmhmghmd	⊢ ( 𝜑 → 𝐹 ∈ ( 𝑆 GrpHom 𝑇 ) )

Proof

Step	Hyp	Ref	Expression
1		lmhmghmd.1	⊢ ( 𝜑 → 𝐹 ∈ ( 𝑆 LMHom 𝑇 ) )
2		lmghm	⊢ ( 𝐹 ∈ ( 𝑆 LMHom 𝑇 ) → 𝐹 ∈ ( 𝑆 GrpHom 𝑇 ) )
3	1 2	syl	⊢ ( 𝜑 → 𝐹 ∈ ( 𝑆 GrpHom 𝑇 ) )