Theorem dfom3 4719

Description: Alias for df-iom 4718. Use it instead of df-iom 4718 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 4718	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Syntax hints:   ∧ wa 104   = wceq 1398   ∈ wcel 2205  {cab 2220  ∀wral 2522  ∅c0 3512  ∩ cint 3954  suc csuc 4491  ωcom 4717

This theorem depends on definitions:  df-iom 4718

This theorem is referenced by:  omex  4720  peano1  4721  peano2  4722  peano5  4725  bj-dfom  16829