Description: There is no set between an ordinal number and its successor. Proposition 7.25 of TakeutiZaring p. 41. (Contributed by NM, 9-Jun-1994)
Ref | Expression | ||
---|---|---|---|
Assertion | onnbtwn | |- ( A e. On -> -. ( A e. B /\ B e. suc A ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eloni | |- ( A e. On -> Ord A ) |
|
2 | ordnbtwn | |- ( Ord A -> -. ( A e. B /\ B e. suc A ) ) |
|
3 | 1 2 | syl | |- ( A e. On -> -. ( A e. B /\ B e. suc A ) ) |