Theorem dfom3 4333

Description: Alias for df-iom 4332. Use it instead of df-iom 4332 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 4332	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Syntax hints:   ∧ wa 102   = wceq 1284   ∈ wcel 1433  {cab 2067  ∀wral 2348  ∅c0 3251  ∩ cint 3636  suc csuc 4120  ωcom 4331

This theorem depends on definitions:  df-iom 4332

This theorem is referenced by:  omex  4334  peano1  4335  peano2  4336  peano5  4339  bj-dfom  10728