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Metamath Proof Explorer

Theorem isofld

Description: An ordered field is a field with a total ordering compatible with its operations. (Contributed by Thierry Arnoux, 23-Mar-2018)

		Ref	Expression
	Assertion	isofld	$⊢ F \in oField \leftrightarrow (F \in Field \land F \in oRing)$

Step	Hyp	Ref	Expression
1		df-ofld	$⊢ oField = Field \cap oRing$
2	1	elin2	$⊢ F \in oField \leftrightarrow (F \in Field \land F \in oRing)$