Definition df-en 6886

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 6893. (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 6883	. 2 class ~~
2		vx	. . . . . 6 setvar x
3	2	cv 1394	. . . . 5 class x
4		vy	. . . . . 6 setvar y
5	4	cv 1394	. . . . 5 class y
6		vf	. . . . . 6 setvar f
7	6	cv 1394	. . . . 5 class f
8	3, 5, 7	wf1o 5316	. . . 4 wff f : x -1-1-onto-> y
9	8, 6	wex 1538	. . 3 wff E. f f : x -1-1-onto-> y
10	9, 2, 4	copab 4143	. 2 class { <. x , y >. | E. f f : x -1-1-onto-> y }
11	1, 10	wceq 1395	1 wff ~~ = { <. x , y >. | E. f f : x -1-1-onto-> y }

This definition is referenced by:  relen  6889  breng  6892  bren  6893  enssdom  6911