Description: A function's value belongs to its range. (Contributed by Glauco Siliprandi, 2-Jan-2022)
Ref | Expression | ||
---|---|---|---|
Hypotheses | fnfvelrnd.1 | |- ( ph -> F Fn A ) |
|
fnfvelrnd.2 | |- ( ph -> B e. A ) |
||
Assertion | fnfvelrnd | |- ( ph -> ( F ` B ) e. ran F ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fnfvelrnd.1 | |- ( ph -> F Fn A ) |
|
2 | fnfvelrnd.2 | |- ( ph -> B e. A ) |
|
3 | fnfvelrn | |- ( ( F Fn A /\ B e. A ) -> ( F ` B ) e. ran F ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> ( F ` B ) e. ran F ) |