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 ) |