Relation between Two Ordinals/Corollary/Proof 1
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Corollary to Relation between Two Ordinals
Let $S$ and $T$ be ordinals.
If $S \ne T$, then either $S$ is an initial segment of $T$, or vice versa.
Proof
By Ordinal Membership is Trichotomy, either $S \in T$ or $T \in S$.
By definition, every element of an ordinal is an initial segment.
Hence the result.
$\blacksquare$