Description: The value of the alternative function at a set as argument equals the function's value at this argument. (Contributed by Alexander van der Vekens, 25-May-2017)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | afvnufveq | |- ( ( F ''' A ) =/= _V -> ( F ''' A ) = ( F ` A ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | afvfundmfveq | |- ( F defAt A -> ( F ''' A ) = ( F ` A ) ) |
|
| 2 | afvnfundmuv | |- ( -. F defAt A -> ( F ''' A ) = _V ) |
|
| 3 | 1 2 | nsyl5 | |- ( -. ( F ''' A ) = ( F ` A ) -> ( F ''' A ) = _V ) |
| 4 | 3 | necon1ai | |- ( ( F ''' A ) =/= _V -> ( F ''' A ) = ( F ` A ) ) |