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Definition df-en 8497
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 8505. (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 8493 . 2 class
2 vx . . . . . 6 setvar 𝑥
32cv 1537 . . . . 5 class 𝑥
4 vy . . . . . 6 setvar 𝑦
54cv 1537 . . . . 5 class 𝑦
6 vf . . . . . 6 setvar 𝑓
76cv 1537 . . . . 5 class 𝑓
83, 5, 7wf1o 6333 . . . 4 wff 𝑓:𝑥1-1-onto𝑦
98, 6wex 1781 . . 3 wff 𝑓 𝑓:𝑥1-1-onto𝑦
109, 2, 4copab 5104 . 2 class {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
111, 10wceq 1538 1 wff ≈ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
Colors of variables: wff setvar class
This definition is referenced by:  relen  8501  bren  8505  enssdom  8521
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