Definition df-en 6754

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 6760. (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 6751	. 2 class ~~
2		vx	. . . . . 6 setvar x
3	2	cv 1362	. . . . 5 class x
4		vy	. . . . . 6 setvar y
5	4	cv 1362	. . . . 5 class y
6		vf	. . . . . 6 setvar f
7	6	cv 1362	. . . . 5 class f
8	3, 5, 7	wf1o 5227	. . . 4 wff f : x -1-1-onto-> y
9	8, 6	wex 1502	. . 3 wff E. f f : x -1-1-onto-> y
10	9, 2, 4	copab 4075	. 2 class { <. x , y >. | E. f f : x -1-1-onto-> y }
11	1, 10	wceq 1363	1 wff ~~ = { <. x , y >. | E. f f : x -1-1-onto-> y }

This definition is referenced by:  relen  6757  bren  6760  enssdom  6775