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Theorem dfnn2 8317
Description: Definition of the set of positive integers. Another name for df-inn 8316. (Contributed by Jeff Hankins, 12-Sep-2013.) (Revised by Mario Carneiro, 3-May-2014.)
Assertion
Ref Expression
dfnn2 ℕ = {𝑥 ∣ (1 ∈ 𝑥 ∧ ∀𝑦𝑥 (𝑦 + 1) ∈ 𝑥)}
Distinct variable group:   𝑥,𝑦

Proof of Theorem dfnn2
StepHypRef Expression
1 df-inn 8316 1 ℕ = {𝑥 ∣ (1 ∈ 𝑥 ∧ ∀𝑦𝑥 (𝑦 + 1) ∈ 𝑥)}
Colors of variables: wff set class
Syntax hints:  wa 102   = wceq 1285  wcel 1434  {cab 2069  wral 2353   cint 3662  (class class class)co 5590  1c1 7253   + caddc 7255  cn 8315
This theorem depends on definitions:  df-inn 8316
This theorem is referenced by:  peano5nni  8318  1nn  8326  peano2nn  8327  arch  8561  caucvgre  10240
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