Definition df-en 4368

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 4377.

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 4364	. 2 class ~~
2		vx	. . . . . 6 set x
3	2	cv 955	. . . . 5 class x
4		vy	. . . . . 6 set y
5	4	cv 955	. . . . 5 class y
6		vf	. . . . . 6 set f
7	6	cv 955	. . . . 5 class f
8	3, 5, 7	wf1o 3181	. . . 4 wff f:x-1-1-onto->y
9	8, 6	wex 980	. . 3 wff E.f f:x-1-1-onto->y
10	9, 2, 4	copab 2666	. 2 class {<.x, y>. | E.f f:x-1-1-onto->y}
11	1, 10	wceq 956	1 wff ~~ = {<.x, y>. | E.f f:x-1-1-onto->y}

This definition is referenced by:  relen 4372  breng 4375  enssdom 4383

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