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Mirrors > Home > ILE Home > Th. List > dfnn2 | GIF version |
Description: Definition of the set of positive integers. Another name for df-inn 8721. (Contributed by Jeff Hankins, 12-Sep-2013.) (Revised by Mario Carneiro, 3-May-2014.) |
Ref | Expression |
---|---|
dfnn2 | ⊢ ℕ = ∩ {𝑥 ∣ (1 ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 (𝑦 + 1) ∈ 𝑥)} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-inn 8721 | 1 ⊢ ℕ = ∩ {𝑥 ∣ (1 ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 (𝑦 + 1) ∈ 𝑥)} |
Colors of variables: wff set class |
Syntax hints: ∧ wa 103 = wceq 1331 ∈ wcel 1480 {cab 2125 ∀wral 2416 ∩ cint 3771 (class class class)co 5774 1c1 7621 + caddc 7623 ℕcn 8720 |
This theorem depends on definitions: df-inn 8721 |
This theorem is referenced by: peano5nni 8723 1nn 8731 peano2nn 8732 arch 8974 caucvgre 10753 |
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