Description: If a set is not in the domain of a class or the class is not a function restricted to the set, then the function value for this set is the universe. (Contributed by Alexander van der Vekens, 26-May-2017)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | afvnfundmuv | |- ( -. F defAt A -> ( F ''' A ) = _V ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | dfafv2 | |- ( F ''' A ) = if ( F defAt A , ( F ` A ) , _V ) |
|
| 2 | iffalse | |- ( -. F defAt A -> if ( F defAt A , ( F ` A ) , _V ) = _V ) |
|
| 3 | 1 2 | syl5eq | |- ( -. F defAt A -> ( F ''' A ) = _V ) |