Theorem dfom3 4696

Description: Alias for df-iom 4695. Use it instead of df-iom 4695 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 4695	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Syntax hints:   ∧ wa 104   = wceq 1398   ∈ wcel 2202  {cab 2217  ∀wral 2511  ∅c0 3496  ∩ cint 3933  suc csuc 4468  ωcom 4694

This theorem depends on definitions:  df-iom 4695

This theorem is referenced by:  omex  4697  peano1  4698  peano2  4699  peano5  4702  bj-dfom  16632