Empty Mapping is Unique

Theorem
For each set $T$ there exists exactly one empty mapping, for which the domain is the empty set:


 * $\varnothing \subseteq \varnothing \times T = \varnothing$

Proof
From Empty Mapping is Mapping, we have that the empty mapping from $\varnothing$ to $T$ exists.

By definition, the empty mapping equals the empty set.

The result follows by Empty Set Unique.