Theorem 0nep0

Description: The empty set and its power set are not equal. (Contributed by NM, 23-Dec-1993)

	Ref	Expression
Assertion	0nep0	$$⊢\varnothing \ne \left\{\varnothing \right\}$$

Proof

Step	Hyp	Ref	Expression
1		0ex	$$⊢\varnothing \in \mathrm{V}$$
2	1	snnz	$$⊢\left\{\varnothing \right\}\ne \varnothing$$
3	2	necomi	$$⊢\varnothing \ne \left\{\varnothing \right\}$$