Definition df-en 6841

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 6848. (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 6838	. 2 class ~~
2		vx	. . . . . 6 setvar x
3	2	cv 1372	. . . . 5 class x
4		vy	. . . . . 6 setvar y
5	4	cv 1372	. . . . 5 class y
6		vf	. . . . . 6 setvar f
7	6	cv 1372	. . . . 5 class f
8	3, 5, 7	wf1o 5279	. . . 4 wff f : x -1-1-onto-> y
9	8, 6	wex 1516	. . 3 wff E. f f : x -1-1-onto-> y
10	9, 2, 4	copab 4112	. 2 class { <. x , y >. | E. f f : x -1-1-onto-> y }
11	1, 10	wceq 1373	1 wff ~~ = { <. x , y >. | E. f f : x -1-1-onto-> y }

This definition is referenced by:  relen  6844  breng  6847  bren  6848  enssdom  6866