This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem ofldfld

Description: An ordered field is a field. (Contributed by Thierry Arnoux, 20-Jan-2018)

		Ref	Expression
	Assertion	ofldfld	$⊢ F \in oField \to F \in Field$

Step	Hyp	Ref	Expression
1		isofld	$⊢ F \in oField \leftrightarrow (F \in Field \land F \in oRing)$
2	1	simplbi	$⊢ F \in oField \to F \in Field$