Description: Cardinal ordering agrees with natural number ordering. Example 3 of Enderton p. 146. (Contributed by NM, 17-Jun-1998)
Ref | Expression | ||
---|---|---|---|
Assertion | nndomo | |- ( ( A e. _om /\ B e. _om ) -> ( A ~<_ B <-> A C_ B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnon | |- ( B e. _om -> B e. On ) |
|
2 | nndomog | |- ( ( A e. _om /\ B e. On ) -> ( A ~<_ B <-> A C_ B ) ) |
|
3 | 1 2 | sylan2 | |- ( ( A e. _om /\ B e. _om ) -> ( A ~<_ B <-> A C_ B ) ) |