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Metamath Proof Explorer

Theorem matgrp

Description: The matrix ring is a group. (Contributed by AV, 21-Dec-2019)

		Ref	Expression
	Hypothesis	matlmod.a	$⊢ A = N Mat R$
	Assertion	matgrp	$⊢ (N \in Fin \land R \in Ring) \to A \in Grp$

Step	Hyp	Ref	Expression
1		matlmod.a	$⊢ A = N Mat R$
2	1	matlmod	$⊢ (N \in Fin \land R \in Ring) \to A \in LMod$
3		lmodgrp	$⊢ A \in LMod \to A \in Grp$
4	2 3	syl	$⊢ (N \in Fin \land R \in Ring) \to A \in Grp$