Theorem 0elpw

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

	Ref	Expression
Assertion	0elpw	⊢ ∅ ∈ 𝒫 𝐴

Proof

Step	Hyp	Ref	Expression
1		0ss	⊢ ∅ ⊆ 𝐴
2		0ex	⊢ ∅ ∈ V
3	2	elpw	⊢ ( ∅ ∈ 𝒫 𝐴 ↔ ∅ ⊆ 𝐴 )
4	1 3	mpbir	⊢ ∅ ∈ 𝒫 𝐴