Theorem dfom3 4624

Description: Alias for df-iom 4623. Use it instead of df-iom 4623 for naming consistency with set.mm. (Contributed by NM, 6-Aug-1994.)

Assertion

Ref	Expression
dfom3	⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Distinct variable group:   𝑥,𝑦

Proof of Theorem dfom3

Step	Hyp	Ref	Expression
1		df-iom 4623	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Syntax hints:   ∧ wa 104   = wceq 1364   ∈ wcel 2164  {cab 2179  ∀wral 2472  ∅c0 3446  ∩ cint 3870  suc csuc 4396  ωcom 4622

This theorem depends on definitions:  df-iom 4623

This theorem is referenced by:  omex  4625  peano1  4626  peano2  4627  peano5  4630  bj-dfom  15425