Definition df-en 4509

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 4518.

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 4505	. 2 class ~~
2		vx	. . . . . 6 set x
3	2	cv 991	. . . . 5 class x
4		vy	. . . . . 6 set y
5	4	cv 991	. . . . 5 class y
6		vf	. . . . . 6 set f
7	6	cv 991	. . . . 5 class f
8	3, 5, 7	wf1o 3262	. . . 4 wff f:x-1-1-onto->y
9	8, 6	wex 1016	. . 3 wff E.f f:x-1-1-onto->y
10	9, 2, 4	copab 2740	. 2 class {<.x, y>. | E.f f:x-1-1-onto->y}
11	1, 10	wceq 992	1 wff ~~ = {<.x, y>. | E.f f:x-1-1-onto->y}

This definition is referenced by:  relen 4513  breng 4516  enssdom 4524

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