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	$$⊢\mathrm{Lim}A\to A=\bigcup A$$

Proof

Step	Hyp	Ref	Expression
1		df-lim	$$⊢\mathrm{Lim}A\leftrightarrow \left(\mathrm{Ord}A\wedge A\ne \varnothing \wedge A=\bigcup A\right)$$
2	1	simp3bi	$$⊢\mathrm{Lim}A\to A=\bigcup A$$