Definition df-drngap 14587

Description: Define class of all division rings. A division ring is a ring in which the relation given by df-apr 14573 is a tight apartness. (Contributed by Jim Kingdon, 29-May-2026.)

Assertion

Ref	Expression
df-drngap	⊢ DivRing = {𝑟 ∈ Ring ∣ (#r‘𝑟) TAp (Base‘𝑟)}

Detailed syntax breakdown of Definition df-drngap

Step	Hyp	Ref	Expression
1		cdr 14585	. 2 class DivRing
2		vr	. . . . . 6 setvar 𝑟
3	2	cv 1401	. . . . 5 class 𝑟
4		cbs 13335	. . . . 5 class Base
5	3, 4	cfv 5375	. . . 4 class (Base‘𝑟)
6		capr 14572	. . . . 5 class #r
7	3, 6	cfv 5375	. . . 4 class (#r‘𝑟)
8	5, 7	wtap 7608	. . 3 wff (#r‘𝑟) TAp (Base‘𝑟)
9		crg 14283	. . 3 class Ring
10	8, 2, 9	crab 2532	. 2 class {𝑟 ∈ Ring ∣ (#r‘𝑟) TAp (Base‘𝑟)}
11	1, 10	wceq 1402	1 wff DivRing = {𝑟 ∈ Ring ∣ (#r‘𝑟) TAp (Base‘𝑟)}

This definition is referenced by:  isdrngtap  14589