Theorem dfom3 4648

Description: Alias for df-iom 4647. Use it instead of df-iom 4647 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 4647	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

Syntax hints:   ∧ wa 104   = wceq 1373   ∈ wcel 2177  {cab 2192  ∀wral 2485  ∅c0 3464  ∩ cint 3891  suc csuc 4420  ωcom 4646

This theorem depends on definitions:  df-iom 4647

This theorem is referenced by:  omex  4649  peano1  4650  peano2  4651  peano5  4654  bj-dfom  16007