Description: If the domain of a function given by maps-to notation is a set, the function is a set. Inference version of mptexg . (Contributed by Glauco Siliprandi, 23-Oct-2021)
Ref | Expression | ||
---|---|---|---|
Hypotheses | mptexf.1 | |- F/_ x A |
|
mptexf.2 | |- A e. _V |
||
Assertion | mptexf | |- ( x e. A |-> B ) e. _V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mptexf.1 | |- F/_ x A |
|
2 | mptexf.2 | |- A e. _V |
|
3 | 1 | mptexgf | |- ( A e. _V -> ( x e. A |-> B ) e. _V ) |
4 | 2 3 | ax-mp | |- ( x e. A |-> B ) e. _V |