Empty Intersection iff Subset of Complement

Theorem

 * $$S \cap T = \varnothing \iff S \subseteq \complement \left({T}\right)$$

where:
 * $$S \cap T$$ denotes the intersection of $$S$$ and $$T$$;
 * $$\varnothing$$ denotes the empty set;
 * $$\complement$$ denotes set complement;
 * $$\subseteq$$ denotes subset;

Proof
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