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Metamath Proof Explorer
Description: A function does not contain the empty set. (Contributed by BJ, 26-Nov-2021)
|
|
Ref |
Expression |
|
Assertion |
0nelfun |
|- ( Fun R -> (/) e/ R ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
funrel |
|- ( Fun R -> Rel R ) |
| 2 |
|
0nelrel |
|- ( Rel R -> (/) e/ R ) |
| 3 |
1 2
|
syl |
|- ( Fun R -> (/) e/ R ) |