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Definition df-en 7819
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 7827. (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 7815 . 2 class
2 vx . . . . . 6 setvar 𝑥
32cv 1473 . . . . 5 class 𝑥
4 vy . . . . . 6 setvar 𝑦
54cv 1473 . . . . 5 class 𝑦
6 vf . . . . . 6 setvar 𝑓
76cv 1473 . . . . 5 class 𝑓
83, 5, 7wf1o 5788 . . . 4 wff 𝑓:𝑥1-1-onto𝑦
98, 6wex 1694 . . 3 wff 𝑓 𝑓:𝑥1-1-onto𝑦
109, 2, 4copab 4636 . 2 class {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
111, 10wceq 1474 1 wff ≈ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
Colors of variables: wff setvar class
This definition is referenced by:  relen  7823  bren  7827  enssdom  7843
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