Theorem dfom3 4625

Description: Alias for df-iom 4624. Use it instead of df-iom 4624 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 4624	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Syntax hints:   ∧ wa 104   = wceq 1364   ∈ wcel 2164  {cab 2179  ∀wral 2472  ∅c0 3447  ∩ cint 3871  suc csuc 4397  ωcom 4623

This theorem depends on definitions:  df-iom 4624

This theorem is referenced by:  omex  4626  peano1  4627  peano2  4628  peano5  4631  bj-dfom  15495