Theorem pwpwpw0

Description: Compute the power set of the power set of the power set of the empty set. (See also pw0 and pwpw0 .) (Contributed by NM, 2-May-2009)

	Ref	Expression
Assertion	pwpwpw0	$$⊢𝒫\left\{\varnothing ,\left\{\varnothing \right\}\right\}=\left\{\varnothing ,\left\{\varnothing \right\}\right\}\cup \left\{\left\{\left\{\varnothing \right\}\right\},\left\{\varnothing ,\left\{\varnothing \right\}\right\}\right\}$$

Proof

Step	Hyp	Ref	Expression
1		pwpr	$$⊢𝒫\left\{\varnothing ,\left\{\varnothing \right\}\right\}=\left\{\varnothing ,\left\{\varnothing \right\}\right\}\cup \left\{\left\{\left\{\varnothing \right\}\right\},\left\{\varnothing ,\left\{\varnothing \right\}\right\}\right\}$$