Definition df-en 6743

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 6749. (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 6740	. 2 class ~~
2		vx	. . . . . 6 setvar x
3	2	cv 1352	. . . . 5 class x
4		vy	. . . . . 6 setvar y
5	4	cv 1352	. . . . 5 class y
6		vf	. . . . . 6 setvar f
7	6	cv 1352	. . . . 5 class f
8	3, 5, 7	wf1o 5217	. . . 4 wff f : x -1-1-onto-> y
9	8, 6	wex 1492	. . 3 wff E. f f : x -1-1-onto-> y
10	9, 2, 4	copab 4065	. 2 class { <. x , y >. | E. f f : x -1-1-onto-> y }
11	1, 10	wceq 1353	1 wff ~~ = { <. x , y >. | E. f f : x -1-1-onto-> y }

This definition is referenced by:  relen  6746  bren  6749  enssdom  6764