Theorem intsn

Description: The intersection of a singleton is its member. Theorem 70 of Suppes p. 41. (Contributed by NM, 29-Sep-2002)

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

Proof

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