Theorem 0elpw

Description: Every power class contains the empty set. (Contributed by NM, 25-Oct-2007)

	Ref	Expression
Assertion	0elpw	$$⊢\varnothing \in 𝒫A$$

Proof

Step	Hyp	Ref	Expression
1		0ss	$$⊢\varnothing \subseteq A$$
2		0ex	$$⊢\varnothing \in \mathrm{V}$$
3	2	elpw	$$⊢\varnothing \in 𝒫A\leftrightarrow \varnothing \subseteq A$$
4	1 3	mpbir	$$⊢\varnothing \in 𝒫A$$