Description: The domain of a mapping is a subset of its base class. (Contributed by Glauco Siliprandi, 23-Oct-2021)
Ref | Expression | ||
---|---|---|---|
Hypotheses | dmmptssf.1 | |- F/_ x A |
|
dmmptssf.2 | |- F = ( x e. A |-> B ) |
||
Assertion | dmmptssf | |- dom F C_ A |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmmptssf.1 | |- F/_ x A |
|
2 | dmmptssf.2 | |- F = ( x e. A |-> B ) |
|
3 | 2 | dmmpt | |- dom F = { x e. A | B e. _V } |
4 | 1 | ssrab2f | |- { x e. A | B e. _V } C_ A |
5 | 3 4 | eqsstri | |- dom F C_ A |