Definition df-en 7569

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 7577. (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 7565	. 2 class ~~
2		vx	. . . . . 6 setvar x
3	2	cv 1436	. . . . 5 class x
4		vy	. . . . . 6 setvar y
5	4	cv 1436	. . . . 5 class y
6		vf	. . . . . 6 setvar f
7	6	cv 1436	. . . . 5 class f
8	3, 5, 7	wf1o 5591	. . . 4 wff f : x -1-1-onto-> y
9	8, 6	wex 1659	. . 3 wff E. f f : x -1-1-onto-> y
10	9, 2, 4	copab 4474	. 2 class { <. x , y >. | E. f f : x -1-1-onto-> y }
11	1, 10	wceq 1437	1 wff ~~ = { <. x , y >. | E. f f : x -1-1-onto-> y }

This definition is referenced by:  relen  7573  bren  7577  enssdom  7592