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Definition df-en 7842
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 7850. (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 7838 . 2 class
2 vx . . . . . 6 setvar 𝑥
32cv 1474 . . . . 5 class 𝑥
4 vy . . . . . 6 setvar 𝑦
54cv 1474 . . . . 5 class 𝑦
6 vf . . . . . 6 setvar 𝑓
76cv 1474 . . . . 5 class 𝑓
83, 5, 7wf1o 5803 . . . 4 wff 𝑓:𝑥1-1-onto𝑦
98, 6wex 1695 . . 3 wff 𝑓 𝑓:𝑥1-1-onto𝑦
109, 2, 4copab 4642 . 2 class {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
111, 10wceq 1475 1 wff ≈ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
Colors of variables: wff setvar class
This definition is referenced by:  relen  7846  bren  7850  enssdom  7866
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