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Definition df-en 8982
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 8991. (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 8978 . 2 class
2 vx . . . . . 6 setvar 𝑥
32cv 1539 . . . . 5 class 𝑥
4 vy . . . . . 6 setvar 𝑦
54cv 1539 . . . . 5 class 𝑦
6 vf . . . . . 6 setvar 𝑓
76cv 1539 . . . . 5 class 𝑓
83, 5, 7wf1o 6558 . . . 4 wff 𝑓:𝑥1-1-onto𝑦
98, 6wex 1779 . . 3 wff 𝑓 𝑓:𝑥1-1-onto𝑦
109, 2, 4copab 5203 . 2 class {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
111, 10wceq 1540 1 wff ≈ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
Colors of variables: wff setvar class
This definition is referenced by:  relen  8986  breng  8990  enssdom  9013
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