Description: A set whose successor is a subset of another class is a member of that class. (Contributed by NM, 16-Sep-1995)
Ref | Expression | ||
---|---|---|---|
Assertion | sucssel | |- ( A e. V -> ( suc A C_ B -> A e. B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sucidg | |- ( A e. V -> A e. suc A ) |
|
2 | ssel | |- ( suc A C_ B -> ( A e. suc A -> A e. B ) ) |
|
3 | 1 2 | syl5com | |- ( A e. V -> ( suc A C_ B -> A e. B ) ) |