Theorem dflim2 4515

Description: Alias for df-ilim 4514. Use it instead of df-ilim 4514 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 4514	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 4507  Lim wlim 4509

This proof depends on definitions:  df-ilim 4514

This theorem is used by:  limeq  4522  nlim0  4539  limord  4540  limuni  4541  0ellim  4543  limon  4660  limom  4761