Theorem dfom3 4683

Description: Alias for df-iom 4682. Use it instead of df-iom 4682 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 4682	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Syntax hints:   ∧ wa 104   = wceq 1395   ∈ wcel 2200  {cab 2215  ∀wral 2508  ∅c0 3491  ∩ cint 3922  suc csuc 4455  ωcom 4681

This theorem depends on definitions:  df-iom 4682

This theorem is referenced by:  omex  4684  peano1  4685  peano2  4686  peano5  4689  bj-dfom  16254