Metamath Proof Explorer


Theorem ordtr

Description: An ordinal class is transitive. (Contributed by NM, 3-Apr-1994)

Ref Expression
Assertion ordtr
|- ( Ord A -> Tr A )

Proof

Step Hyp Ref Expression
1 df-ord
 |-  ( Ord A <-> ( Tr A /\ _E We A ) )
2 1 simplbi
 |-  ( Ord A -> Tr A )