Ordinal is Subset of Class of All Ordinals

From ProofWiki
Jump to navigation Jump to search

Theorem

Suppose $A$ is an ordinal.

Then:

$A \subseteq \On$

where $\On$ represents the class of all ordinals.


Proof

By Ordinal is Member of Class of All Ordinals:

$A \in \On \lor A = \On$

In either case:

$A \subseteq \On$

since $\On$ is transitive.




Sources