Definition df-drngap 14606

Description: Define class of all division rings. A division ring is a ring in which the relation given by df-apr 14592 is a tight apartness. (Contributed by Jim Kingdon, 29-May-2026.)

Assertion

Ref	Expression
df-drngap	|- DivRing = { r e. Ring | (#r ` r ) TAp ( Base ` r ) }

Detailed syntax breakdown of Definition df-drngap

Step	Hyp	Ref	Expression
1		cdr 14604	. 2 class DivRing
2		vr	. . . . . 6 setvar r
3	2	cv 1401	. . . . 5 class r
4		cbs 13354	. . . . 5 class Base
5	3, 4	cfv 5377	. . . 4 class ( Base ` r )
6		capr 14591	. . . . 5 class #r
7	3, 6	cfv 5377	. . . 4 class (#r ` r )
8	5, 7	wtap 7614	. . 3 wff (#r ` r ) TAp ( Base ` r )
9		crg 14302	. . 3 class Ring
10	8, 2, 9	crab 2532	. 2 class { r e. Ring | (#r ` r ) TAp ( Base ` r ) }
11	1, 10	wceq 1402	1 wff DivRing = { r e. Ring | (#r ` r ) TAp ( Base ` r ) }

This definition is used by:  isdrngtap  14608