Description: An onto function implies dominance of domain over range. (Contributed by NM, 23-Jul-2004)
Ref | Expression | ||
---|---|---|---|
Hypothesis | fodom.1 | |- A e. _V |
|
Assertion | fodom | |- ( F : A -onto-> B -> B ~<_ A ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fodom.1 | |- A e. _V |
|
2 | fodomg | |- ( A e. _V -> ( F : A -onto-> B -> B ~<_ A ) ) |
|
3 | 1 2 | ax-mp | |- ( F : A -onto-> B -> B ~<_ A ) |