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Definition df-en 8499
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 8507. (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 8495 . 2 class
2 vx . . . . . 6 setvar 𝑥
32cv 1527 . . . . 5 class 𝑥
4 vy . . . . . 6 setvar 𝑦
54cv 1527 . . . . 5 class 𝑦
6 vf . . . . . 6 setvar 𝑓
76cv 1527 . . . . 5 class 𝑓
83, 5, 7wf1o 6348 . . . 4 wff 𝑓:𝑥1-1-onto𝑦
98, 6wex 1771 . . 3 wff 𝑓 𝑓:𝑥1-1-onto𝑦
109, 2, 4copab 5120 . 2 class {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
111, 10wceq 1528 1 wff ≈ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
Colors of variables: wff setvar class
This definition is referenced by:  relen  8503  bren  8507  enssdom  8523
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