Theorem dfom3 4628

Description: Alias for df-iom 4627. Use it instead of df-iom 4627 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 4627	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Syntax hints:   ∧ wa 104   = wceq 1364   ∈ wcel 2167  {cab 2182  ∀wral 2475  ∅c0 3450  ∩ cint 3874  suc csuc 4400  ωcom 4626

This theorem depends on definitions:  df-iom 4627

This theorem is referenced by:  omex  4629  peano1  4630  peano2  4631  peano5  4634  bj-dfom  15579