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Definition df-en 6410
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 6416. (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 6407 . 2 class
2 vx . . . . . 6 setvar 𝑥
32cv 1286 . . . . 5 class 𝑥
4 vy . . . . . 6 setvar 𝑦
54cv 1286 . . . . 5 class 𝑦
6 vf . . . . . 6 setvar 𝑓
76cv 1286 . . . . 5 class 𝑓
83, 5, 7wf1o 4980 . . . 4 wff 𝑓:𝑥1-1-onto𝑦
98, 6wex 1424 . . 3 wff 𝑓 𝑓:𝑥1-1-onto𝑦
109, 2, 4copab 3873 . 2 class {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
111, 10wceq 1287 1 wff ≈ = {⟨𝑥, 𝑦⟩ ∣ ∃𝑓 𝑓:𝑥1-1-onto𝑦}
Colors of variables: wff set class
This definition is referenced by:  relen  6413  bren  6416  enssdom  6431
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