Description: Elementhood in an image set. (Contributed by Glauco Siliprandi, 23-Oct-2021)
Ref | Expression | ||
---|---|---|---|
Hypotheses | elrnmpt1d.1 | |- F = ( x e. A |-> B ) |
|
elrnmpt1d.2 | |- ( ph -> x e. A ) |
||
elrnmpt1d.3 | |- ( ph -> B e. V ) |
||
Assertion | elrnmpt1d | |- ( ph -> B e. ran F ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elrnmpt1d.1 | |- F = ( x e. A |-> B ) |
|
2 | elrnmpt1d.2 | |- ( ph -> x e. A ) |
|
3 | elrnmpt1d.3 | |- ( ph -> B e. V ) |
|
4 | 1 | elrnmpt1 | |- ( ( x e. A /\ B e. V ) -> B e. ran F ) |
5 | 2 3 4 | syl2anc | |- ( ph -> B e. ran F ) |