Definition df-en 6698

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 6704. (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 6695	. 2 class ~~
2		vx	. . . . . 6 setvar x
3	2	cv 1341	. . . . 5 class x
4		vy	. . . . . 6 setvar y
5	4	cv 1341	. . . . 5 class y
6		vf	. . . . . 6 setvar f
7	6	cv 1341	. . . . 5 class f
8	3, 5, 7	wf1o 5181	. . . 4 wff f : x -1-1-onto-> y
9	8, 6	wex 1479	. . 3 wff E. f f : x -1-1-onto-> y
10	9, 2, 4	copab 4036	. 2 class { <. x , y >. | E. f f : x -1-1-onto-> y }
11	1, 10	wceq 1342	1 wff ~~ = { <. x , y >. | E. f f : x -1-1-onto-> y }

This definition is referenced by:  relen  6701  bren  6704  enssdom  6719