Metamath Proof Explorer


Theorem ontr

Description: An ordinal number is a transitive class. (Contributed by NM, 11-Jun-1994) Put in closed form. (Resised by BJ, 28-Dec-2024.)

Ref Expression
Assertion ontr A On Tr A

Proof

Step Hyp Ref Expression
1 eloni A On Ord A
2 ordtr Ord A Tr A
3 1 2 syl A On Tr A