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Metamath Proof Explorer

Theorem prrngorngo

Description: A prime ring is a ring. (Contributed by Jeff Madsen, 10-Jun-2010)

		Ref	Expression
	Assertion	prrngorngo	$⊢ R \in PrRing \to R \in RingOps$

Step	Hyp	Ref	Expression
1		eqid	$⊢ 1^{st} (R) = 1^{st} (R)$
2		eqid	$⊢ GId (1^{st} (R)) = GId (1^{st} (R))$
3	1 2	isprrngo	$⊢ R \in PrRing \leftrightarrow (R \in RingOps \land \{GId (1^{st} (R))\} \in PrIdl (R))$
4	3	simplbi	$⊢ R \in PrRing \to R \in RingOps$