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 ∈ oField ↔ ( 𝐹 ∈ Field ∧ 𝐹 ∈ oRing ) )

Proof

Step	Hyp	Ref	Expression
1		df-ofld	⊢ oField = ( Field ∩ oRing )
2	1	elin2	⊢ ( 𝐹 ∈ oField ↔ ( 𝐹 ∈ Field ∧ 𝐹 ∈ oRing ) )