Theorem unisn

Description: A set equals the union of its singleton. Theorem 8.2 of Quine p. 53. (Contributed by NM, 30-Aug-1993)

	Ref	Expression
Hypothesis	unisn.1	$$⊢A\in \mathrm{V}$$
Assertion	unisn	$$⊢\bigcup \left\{A\right\}=A$$

Proof

Step	Hyp	Ref	Expression
1		unisn.1	$$⊢A\in \mathrm{V}$$
2		unisng	$$⊢A\in \mathrm{V}\to \bigcup \left\{A\right\}=A$$
3	1 2	ax-mp	$$⊢\bigcup \left\{A\right\}=A$$