Cartesian Product is Empty iff Factor is Empty

Theorem

 * $S \times T = \varnothing \iff S = \varnothing \lor T = \varnothing$.

Thus:
 * $S \times \varnothing = \varnothing = \varnothing \times T$

Proof
So by the Rule of Transposition:
 * $S = \varnothing \lor T = \varnothing \iff S \times T = \varnothing$