Theorem dfom3 4690

Description: Alias for df-iom 4689. Use it instead of df-iom 4689 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 4689	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Syntax hints:   ∧ wa 104   = wceq 1397   ∈ wcel 2202  {cab 2217  ∀wral 2510  ∅c0 3494  ∩ cint 3928  suc csuc 4462  ωcom 4688

This theorem depends on definitions:  df-iom 4689

This theorem is referenced by:  omex  4691  peano1  4692  peano2  4693  peano5  4696  bj-dfom  16528