Description: An ordinal number is an ordinal set. (Contributed by NM, 5-Jun-1994)
Ref | Expression | ||
---|---|---|---|
Assertion | elong | |- ( A e. V -> ( A e. On <-> Ord A ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ordeq | |- ( y = x -> ( Ord y <-> Ord x ) ) |
|
2 | ordeq | |- ( x = A -> ( Ord x <-> Ord A ) ) |
|
3 | df-on | |- On = { y | Ord y } |
|
4 | 1 2 3 | elab2gw | |- ( A e. V -> ( A e. On <-> Ord A ) ) |