Theorem pp0ex

Description: The power set of the power set of the empty set (the ordinal 2) is a set. (Contributed by NM, 24-Jun-1993)

	Ref	Expression
Assertion	pp0ex	⊢ { ∅ , { ∅ } } ∈ V

Proof

Step	Hyp	Ref	Expression
1		pwpw0	⊢ 𝒫 { ∅ } = { ∅ , { ∅ } }
2		p0ex	⊢ { ∅ } ∈ V
3	2	pwex	⊢ 𝒫 { ∅ } ∈ V
4	1 3	eqeltrri	⊢ { ∅ , { ∅ } } ∈ V