Theorem dfom3 4501

Description: Alias for df-iom 4500. Use it instead of df-iom 4500 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 4500	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Syntax hints:   ∧ wa 103   = wceq 1331   ∈ wcel 1480  {cab 2123  ∀wral 2414  ∅c0 3358  ∩ cint 3766  suc csuc 4282  ωcom 4499

This theorem depends on definitions:  df-iom 4500

This theorem is referenced by:  omex  4502  peano1  4503  peano2  4504  peano5  4507  bj-dfom  13120