nrgtgp

Description: A normed ring is a topological group. (Contributed by Mario Carneiro, 5-Oct-2015)

		Ref	Expression
	Assertion	nrgtgp	$⊢ R \in NrmRing \to R \in TopGrp$

Step	Hyp	Ref	Expression
1		nrgngp	$⊢ R \in NrmRing \to R \in NrmGrp$
2		nrgring	$⊢ R \in NrmRing \to R \in Ring$
3		ringabl	$⊢ R \in Ring \to R \in Abel$
4	2 3	syl	$⊢ R \in NrmRing \to R \in Abel$
5		ngptgp	$⊢ (R \in NrmGrp \land R \in Abel) \to R \in TopGrp$
6	1 4 5	syl2anc	$⊢ R \in NrmRing \to R \in TopGrp$

Metamath Proof Explorer