Theorem dfom3 4315

Description: Alias for df-iom 4314. Use it instead of df-iom 4314 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 4314	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Syntax hints:   ∧ wa 97   = wceq 1243   ∈ wcel 1393  {cab 2026  ∀wral 2306  ∅c0 3224  ∩ cint 3615  suc csuc 4102  ωcom 4313

This theorem depends on definitions:  df-iom 4314

This theorem is referenced by:  omex  4316  peano1  4317  peano2  4318  peano5  4321  bj-dfom  10057