Theorem dfom3 4638

Description: Alias for df-iom 4637. Use it instead of df-iom 4637 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 4637	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Syntax hints:   ∧ wa 104   = wceq 1372   ∈ wcel 2175  {cab 2190  ∀wral 2483  ∅c0 3459  ∩ cint 3884  suc csuc 4410  ωcom 4636

This theorem depends on definitions:  df-iom 4637

This theorem is referenced by:  omex  4639  peano1  4640  peano2  4641  peano5  4644  bj-dfom  15733