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	$$⊢\left\{\varnothing \right\}\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		pw0	$$⊢𝒫\varnothing =\left\{\varnothing \right\}$$
2		0ex	$$⊢\varnothing \in \mathrm{V}$$
3	2	pwex	$$⊢𝒫\varnothing \in \mathrm{V}$$
4	1 3	eqeltrri	$$⊢\left\{\varnothing \right\}\in \mathrm{V}$$