Description: If a class is a function restricted to a member of its domain, then the function value for this member is equal for both definitions. (Contributed by Alexander van der Vekens, 25-May-2017)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | afvfundmfveq | |- ( F defAt A -> ( F ''' A ) = ( F ` A ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | dfafv2 | |- ( F ''' A ) = if ( F defAt A , ( F ` A ) , _V ) |
|
| 2 | iftrue | |- ( F defAt A -> if ( F defAt A , ( F ` A ) , _V ) = ( F ` A ) ) |
|
| 3 | 1 2 | syl5eq | |- ( F defAt A -> ( F ''' A ) = ( F ` A ) ) |