ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-en Structured version   GIF version

Definition df-en 6158
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 6164. (Contributed by NM, 28-Mar-1998.)
Assertion
Ref Expression
df-en ≈ = {⟨x, y⟩ ∣ f f:x1-1-ontoy}
Distinct variable group:   x,y,f

Detailed syntax breakdown of Definition df-en
StepHypRef Expression
1 cen 6155 . 2 class
2 vx . . . . . 6 setvar x
32cv 1241 . . . . 5 class x
4 vy . . . . . 6 setvar y
54cv 1241 . . . . 5 class y
6 vf . . . . . 6 setvar f
76cv 1241 . . . . 5 class f
83, 5, 7wf1o 4844 . . . 4 wff f:x1-1-ontoy
98, 6wex 1378 . . 3 wff f f:x1-1-ontoy
109, 2, 4copab 3808 . 2 class {⟨x, y⟩ ∣ f f:x1-1-ontoy}
111, 10wceq 1242 1 wff ≈ = {⟨x, y⟩ ∣ f f:x1-1-ontoy}
Colors of variables: wff set class
This definition is referenced by:  relen  6161  bren  6164  enssdom  6178
  Copyright terms: Public domain W3C validator