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# Let <math>\Omega</math> be a set that contains all ordinal numbers.
# <math>\Omega</math> is [[Transitive set|transitive]] because for every element <math>x</math> of <math>\Omega</math> (which is an ordinal number and can be any ordinal number) and every element <math>y</math> of <math>x</math> (i.e. under the definition of [[Von Neumann
# <math>\Omega</math> is well ordered by the membership relation because all its elements are also well ordered by this relation.
# So, by steps 2 and 3, we have that <math>\Omega</math> is an ordinal class and also, by step 1, an ordinal number, because all ordinal classes that are sets are also ordinal numbers.
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