Definition df-rusgr 26454

Description: Define the "k-regular simple graph" predicate, which is true for a simple graph being k-regular: read G RegUSGraph K as G is a K-regular simple graph. (Contributed by Alexander van der Vekens, 6-Jul-2018.) (Revised by AV, 18-Dec-2020.)

Assertion

Ref	Expression
df-rusgr	|- RegUSGraph = { <. g , k >. | ( g e. USGraph /\ g RegGraph k ) }

Distinct variable group:   g, k

Detailed syntax breakdown of Definition df-rusgr

Step	Hyp	Ref	Expression
1		crusgr 26452	. 2 class RegUSGraph
2		vg	. . . . . 6 setvar g
3	2	cv 1482	. . . . 5 class g
4		cusgr 26044	. . . . 5 class USGraph
5	3, 4	wcel 1990	. . . 4 wff g e. USGraph
6		vk	. . . . . 6 setvar k
7	6	cv 1482	. . . . 5 class k
8		crgr 26451	. . . . 5 class RegGraph
9	3, 7, 8	wbr 4653	. . . 4 wff g RegGraph k
10	5, 9	wa 384	. . 3 wff ( g e. USGraph /\ g RegGraph k )
11	10, 2, 6	copab 4712	. 2 class { <. g , k >. | ( g e. USGraph /\ g RegGraph k ) }
12	1, 11	wceq 1483	1 wff RegUSGraph = { <. g , k >. | ( g e. USGraph /\ g RegGraph k ) }

This definition is referenced by:  isrusgr  26457  rusgrprop  26458