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Definition df-en 8309
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 8317. (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 8305 . 2 class
2 vx . . . . . 6 setvar 𝑥
32cv 1506 . . . . 5 class 𝑥
4 vy . . . . . 6 setvar 𝑦
54cv 1506 . . . . 5 class 𝑦
6 vf . . . . . 6 setvar 𝑓
76cv 1506 . . . . 5 class 𝑓
83, 5, 7wf1o 6189 . . . 4 wff 𝑓:𝑥1-1-onto𝑦
98, 6wex 1742 . . 3 wff 𝑓 𝑓:𝑥1-1-onto𝑦
109, 2, 4copab 4992 . 2 class {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
111, 10wceq 1507 1 wff ≈ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
Colors of variables: wff setvar class
This definition is referenced by:  relen  8313  bren  8317  enssdom  8333
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