Theorem dfom3 4464

Description: Alias for df-iom 4463. Use it instead of df-iom 4463 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 4463	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Syntax hints:   ∧ wa 103   = wceq 1312   ∈ wcel 1461  {cab 2099  ∀wral 2388  ∅c0 3327  ∩ cint 3735  suc csuc 4245  ωcom 4462

This theorem depends on definitions:  df-iom 4463

This theorem is referenced by:  omex  4465  peano1  4466  peano2  4467  peano5  4470  bj-dfom  12814