Definition df-en 6222

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 6228. (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 6219	. 2 class ~~
2		vx	. . . . . 6 setvar x
3	2	cv 1242	. . . . 5 class x
4		vy	. . . . . 6 setvar y
5	4	cv 1242	. . . . 5 class y
6		vf	. . . . . 6 setvar f
7	6	cv 1242	. . . . 5 class f
8	3, 5, 7	wf1o 4901	. . . 4 wff f : x -1-1-onto-> y
9	8, 6	wex 1381	. . 3 wff E. f f : x -1-1-onto-> y
10	9, 2, 4	copab 3817	. 2 class { <. x , y >. | E. f f : x -1-1-onto-> y }
11	1, 10	wceq 1243	1 wff ~~ = { <. x , y >. | E. f f : x -1-1-onto-> y }

This definition is referenced by:  relen  6225  bren  6228  enssdom  6242