Theorem onunisuci

Description: An ordinal number is equal to the union of its successor. (Contributed by NM, 12-Jun-1994)

	Ref	Expression
Hypothesis	on.1	$$⊢A\in \mathrm{On}$$
Assertion	onunisuci	$$⊢\bigcup \mathrm{suc}A=A$$

Proof

Step	Hyp	Ref	Expression
1		on.1	$$⊢A\in \mathrm{On}$$
2	1	ontrci	$$⊢\mathrm{Tr}A$$
3	1	elexi	$$⊢A\in \mathrm{V}$$
4	3	unisuc	$$⊢\mathrm{Tr}A\leftrightarrow \bigcup \mathrm{suc}A=A$$
5	2 4	mpbi	$$⊢\bigcup \mathrm{suc}A=A$$