Theorem limuni

Description: A limit ordinal is its own supremum (union). Lemma 2.13 of Schloeder p. 5. (Contributed by NM, 4-May-1995)

	Ref	Expression
Assertion	limuni	⊢ ( Lim 𝐴 → 𝐴 = ∪ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		df-lim	⊢ ( Lim 𝐴 ↔ ( Ord 𝐴 ∧ 𝐴 ≠ ∅ ∧ 𝐴 = ∪ 𝐴 ) )
2	1	simp3bi	⊢ ( Lim 𝐴 → 𝐴 = ∪ 𝐴 )