Definition df-en 7601

Description: Define the equinumerosity relation. Definition of [Enderton] p. 129. We define ~~ to be a binary relation rather than a connective, so its arguments must be sets to be meaningful. This is acceptable because we do not consider equinumerosity for proper classes. We derive the usual definition as bren 7609. (Contributed by NM, 28-Mar-1998.)

Assertion

Ref	Expression
df-en	|- ~~ = { <. x , y >. | E. f f : x -1-1-onto-> y }

Distinct variable group:   x, y, f

Detailed syntax breakdown of Definition df-en

Step	Hyp	Ref	Expression
1		cen 7597	. 2 class ~~
2		vx	. . . . . 6 setvar x
3	2	cv 1454	. . . . 5 class x
4		vy	. . . . . 6 setvar y
5	4	cv 1454	. . . . 5 class y
6		vf	. . . . . 6 setvar f
7	6	cv 1454	. . . . 5 class f
8	3, 5, 7	wf1o 5604	. . . 4 wff f : x -1-1-onto-> y
9	8, 6	wex 1674	. . 3 wff E. f f : x -1-1-onto-> y
10	9, 2, 4	copab 4476	. 2 class { <. x , y >. | E. f f : x -1-1-onto-> y }
11	1, 10	wceq 1455	1 wff ~~ = { <. x , y >. | E. f f : x -1-1-onto-> y }

This definition is referenced by:  relen  7605  bren  7609  enssdom  7625