Metamath Proof Explorer
Description: Membership inference from subclass relationship. (Contributed by NM, 31-May-1999)
|
|
Ref |
Expression |
|
Hypotheses |
sseli.1 |
|- A C_ B |
|
|
sselii.2 |
|- C e. A |
|
Assertion |
sselii |
|- C e. B |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
sseli.1 |
|- A C_ B |
| 2 |
|
sselii.2 |
|- C e. A |
| 3 |
1
|
sseli |
|- ( C e. A -> C e. B ) |
| 4 |
2 3
|
ax-mp |
|- C e. B |