Theorem dfom3 4576

Description: Alias for df-iom 4575. Use it instead of df-iom 4575 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 4575	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Syntax hints:   ∧ wa 103   = wceq 1348   ∈ wcel 2141  {cab 2156  ∀wral 2448  ∅c0 3414  ∩ cint 3831  suc csuc 4350  ωcom 4574

This theorem depends on definitions:  df-iom 4575

This theorem is referenced by:  omex  4577  peano1  4578  peano2  4579  peano5  4582  bj-dfom  13968