Description: The class of natural numbers is a subclass of the class of non-limit ordinal numbers. Exercise 4 of TakeutiZaring p. 42. (Contributed by NM, 2-Nov-2004) (Proof shortened by Andrew Salmon, 27-Aug-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | omssnlim | |- _om C_ { x e. On | -. Lim x } |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | omsson | |- _om C_ On |
|
2 | nnlim | |- ( x e. _om -> -. Lim x ) |
|
3 | 2 | rgen | |- A. x e. _om -. Lim x |
4 | ssrab | |- ( _om C_ { x e. On | -. Lim x } <-> ( _om C_ On /\ A. x e. _om -. Lim x ) ) |
|
5 | 1 3 4 | mpbir2an | |- _om C_ { x e. On | -. Lim x } |