Theorem relfldext

Description: The field extension is a relation. (Contributed by Thierry Arnoux, 29-Jul-2023)

	Ref	Expression
Assertion	relfldext	$$⊢\mathrm{Rel}{/}_{\mathrm{FldExt}}$$

Proof

Step	Hyp	Ref	Expression
1		df-fldext	$$⊢{/}_{\mathrm{FldExt}}=\left\{⟨e,f⟩|\left(\left(e\in \mathrm{Field}\wedge f\in \mathrm{Field}\right)\wedge \left(f=e{\upharpoonright }_{𝑠}{\mathrm{Base}}_f\wedge {\mathrm{Base}}_f\in \mathrm{SubRing}\left(e\right)\right)\right)\right\}$$
2	1	relopabiv	$$⊢\mathrm{Rel}{/}_{\mathrm{FldExt}}$$