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Definition df-prm 15166
Description: Define the set of prime numbers. (Contributed by Paul Chapman, 22-Jun-2011.)
Assertion
Ref Expression
df-prm ℙ = {𝑝 ∈ ℕ ∣ {𝑛 ∈ ℕ ∣ 𝑛𝑝} ≈ 2𝑜}
Distinct variable group:   𝑛,𝑝

Detailed syntax breakdown of Definition df-prm
StepHypRef Expression
1 cprime 15165 . 2 class
2 vn . . . . . . 7 setvar 𝑛
32cv 1473 . . . . . 6 class 𝑛
4 vp . . . . . . 7 setvar 𝑝
54cv 1473 . . . . . 6 class 𝑝
6 cdvds 14763 . . . . . 6 class
73, 5, 6wbr 4573 . . . . 5 wff 𝑛𝑝
8 cn 10863 . . . . 5 class
97, 2, 8crab 2895 . . . 4 class {𝑛 ∈ ℕ ∣ 𝑛𝑝}
10 c2o 7414 . . . 4 class 2𝑜
11 cen 7811 . . . 4 class
129, 10, 11wbr 4573 . . 3 wff {𝑛 ∈ ℕ ∣ 𝑛𝑝} ≈ 2𝑜
1312, 4, 8crab 2895 . 2 class {𝑝 ∈ ℕ ∣ {𝑛 ∈ ℕ ∣ 𝑛𝑝} ≈ 2𝑜}
141, 13wceq 1474 1 wff ℙ = {𝑝 ∈ ℕ ∣ {𝑛 ∈ ℕ ∣ 𝑛𝑝} ≈ 2𝑜}
Colors of variables: wff setvar class
This definition is referenced by:  isprm  15167
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