Definition df-en 4374

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 4383.

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 4370	. 2 class ~~
2		vx	. . . . . 6 set x
3	2	cv 957	. . . . 5 class x
4		vy	. . . . . 6 set y
5	4	cv 957	. . . . 5 class y
6		vf	. . . . . 6 set f
7	6	cv 957	. . . . 5 class f
8	3, 5, 7	wf1o 3187	. . . 4 wff f:x-1-1-onto->y
9	8, 6	wex 982	. . 3 wff E.f f:x-1-1-onto->y
10	9, 2, 4	copab 2671	. 2 class {<.x, y>. | E.f f:x-1-1-onto->y}
11	1, 10	wceq 958	1 wff ~~ = {<.x, y>. | E.f f:x-1-1-onto->y}

This definition is referenced by:  relen 4378  breng 4381  enssdom 4389

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