Description: Relationship between subset and membership of an ordinal number. (Contributed by NM, 15-Sep-1995)
Ref | Expression | ||
---|---|---|---|
Assertion | onsseleq | |- ( ( A e. On /\ B e. On ) -> ( A C_ B <-> ( A e. B \/ A = B ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eloni | |- ( A e. On -> Ord A ) |
|
2 | eloni | |- ( B e. On -> Ord B ) |
|
3 | ordsseleq | |- ( ( Ord A /\ Ord B ) -> ( A C_ B <-> ( A e. B \/ A = B ) ) ) |
|
4 | 1 2 3 | syl2an | |- ( ( A e. On /\ B e. On ) -> ( A C_ B <-> ( A e. B \/ A = B ) ) ) |