Description: Membership implication from subclass relationship. (Contributed by NM, 5-Aug-1993)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | sseli.1 | |- A C_ B |
|
| Assertion | sseli | |- ( C e. A -> C e. B ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sseli.1 | |- A C_ B |
|
| 2 | ssel | |- ( A C_ B -> ( C e. A -> C e. B ) ) |
|
| 3 | 1 2 | ax-mp | |- ( C e. A -> C e. B ) |