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	$$⊢F\in \mathrm{oField}\leftrightarrow \left(F\in \mathrm{Field}\wedge F\in \mathrm{oRing}\right)$$

Proof

Step	Hyp	Ref	Expression
1		df-ofld	$$⊢\mathrm{oField}=\mathrm{Field}\cap \mathrm{oRing}$$
2	1	elin2	$$⊢F\in \mathrm{oField}\leftrightarrow \left(F\in \mathrm{Field}\wedge F\in \mathrm{oRing}\right)$$