Definition df-en 6030

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 6031. (Contributed by NM, 28-Mar-1998.)

Assertion

Ref	Expression
df-en	⊢ ≈ = {⟨x, y⟩ ∣ ∃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 6029	. 2 class ≈
2		vx	. . . . . 6 setvar x
3	2	cv 1641	. . . . 5 class x
4		vy	. . . . . 6 setvar y
5	4	cv 1641	. . . . 5 class y
6		vf	. . . . . 6 setvar f
7	6	cv 1641	. . . . 5 class f
8	3, 5, 7	wf1o 4781	. . . 4 wff f:x–1-1-onto→y
9	8, 6	wex 1541	. . 3 wff ∃f f:x–1-1-onto→y
10	9, 2, 4	copab 4623	. 2 class {⟨x, y⟩ ∣ ∃f f:x–1-1-onto→y}
11	1, 10	wceq 1642	1 wff ≈ = {⟨x, y⟩ ∣ ∃f f:x–1-1-onto→y}

This definition is referenced by:  bren  6031  enex  6032