Theorem dflim2 4517

Description: Alias for df-ilim 4516. Use it instead of df-ilim 4516 for naming consistency with set.mm. (Contributed by NM, 4-Nov-2004.)

Assertion

Ref	Expression
dflim2	⊢ (Lim 𝐴 ↔ (Ord 𝐴 ∧ ∅ ∈ 𝐴 ∧ 𝐴 = ∪ 𝐴))

Proof of Theorem dflim2

Step	Hyp	Ref	Expression
1		df-ilim 4516	1 ⊢ (Lim 𝐴 ↔ (Ord 𝐴 ∧ ∅ ∈ 𝐴 ∧ 𝐴 = ∪ 𝐴))

This proof depends on syntax axioms:   ↔ wb 105   ∧ w3a 1009   = wceq 1402   ∈ wcel 2209  ∅c0 3520  ∪ cuni 3935  Ord word 4509  Lim wlim 4511

This proof depends on definitions:  df-ilim 4516

This theorem is used by:  limeq  4524  nlim0  4541  limord  4542  limuni  4543  0ellim  4545  limon  4662  limom  4763