Theorem p0ex

Description: The power set of the empty set (the ordinal 1) is a set. See also p0exALT . (Contributed by NM, 23-Dec-1993)

	Ref	Expression
Assertion	p0ex	⊢ { ∅ } ∈ V

Proof

Step	Hyp	Ref	Expression
1		pw0	⊢ 𝒫 ∅ = { ∅ }
2		0ex	⊢ ∅ ∈ V
3	2	pwex	⊢ 𝒫 ∅ ∈ V
4	1 3	eqeltrri	⊢ { ∅ } ∈ V