Theorem dfom3 4569

Description: Alias for df-iom 4568. Use it instead of df-iom 4568 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 4568	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Syntax hints:   ∧ wa 103   = wceq 1343   ∈ wcel 2136  {cab 2151  ∀wral 2444  ∅c0 3409  ∩ cint 3824  suc csuc 4343  ωcom 4567

This theorem depends on definitions:  df-iom 4568

This theorem is referenced by:  omex  4570  peano1  4571  peano2  4572  peano5  4575  bj-dfom  13825