Subset of Empty Set

Theorem
Let $A$ be a class.

Then:
 * $A$ is a subset of the empty set $\varnothing$


 * $A$ is equal to the empty set:
 * $A$ is equal to the empty set:


 * $\displaystyle A \subseteq \varnothing \iff A = \varnothing$

Proof
Conversely: