Theorem dfom3 4714

Description: Alias for df-iom 4713. Use it instead of df-iom 4713 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 4713	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Syntax hints:   ∧ wa 104   = wceq 1398   ∈ wcel 2203  {cab 2218  ∀wral 2520  ∅c0 3508  ∩ cint 3949  suc csuc 4486  ωcom 4712

This theorem depends on definitions:  df-iom 4713

This theorem is referenced by:  omex  4715  peano1  4716  peano2  4717  peano5  4720  bj-dfom  16703