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 e. On -> Tr A )

Proof

Step Hyp Ref Expression
1 eloni 
 |-  ( A e. On -> Ord A )
2 ordtr 
 |-  ( Ord A -> Tr A )
3 1 2 syl 
 |-  ( A e. On -> Tr A )