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Definition df-en 7998
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 8006. (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 7994 . 2 class
2 vx . . . . . 6 setvar 𝑥
32cv 1522 . . . . 5 class 𝑥
4 vy . . . . . 6 setvar 𝑦
54cv 1522 . . . . 5 class 𝑦
6 vf . . . . . 6 setvar 𝑓
76cv 1522 . . . . 5 class 𝑓
83, 5, 7wf1o 5925 . . . 4 wff 𝑓:𝑥1-1-onto𝑦
98, 6wex 1744 . . 3 wff 𝑓 𝑓:𝑥1-1-onto𝑦
109, 2, 4copab 4745 . 2 class {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
111, 10wceq 1523 1 wff ≈ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
Colors of variables: wff setvar class
This definition is referenced by:  relen  8002  bren  8006  enssdom  8022
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