Theorem dfom3 4739

Description: Alias for df-iom 4738. Use it instead of df-iom 4738 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 4738	1 ⊢ ω = ∩ {𝑥 ∣ (∅ ∈ 𝑥 ∧ ∀𝑦 ∈ 𝑥 suc 𝑦 ∈ 𝑥)}

This proof depends on syntax axioms:   ∧ wa 104   = wceq 1402   ∈ wcel 2209  {cab 2224  ∀wral 2528  ∅c0 3520  ∩ cint 3970  suc csuc 4510  ωcom 4737

This proof depends on definitions:  df-iom 4738

This theorem is used by:  omex  4740  peano1  4741  peano2  4742  peano5  4745  bj-dfom  16959