Theorem dfom3 4587

Description: Alias for df-iom 4586. Use it instead of df-iom 4586 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 4586	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Syntax hints:   ∧ wa 104   = wceq 1353   ∈ wcel 2148  {cab 2163  ∀wral 2455  ∅c0 3422  ∩ cint 3842  suc csuc 4361  ωcom 4585

This theorem depends on definitions:  df-iom 4586

This theorem is referenced by:  omex  4588  peano1  4589  peano2  4590  peano5  4593  bj-dfom  14307