Description: An operation's value belongs to its codomain. (Contributed by Mario Carneiro, 29-Dec-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | fovcdmd.1 | |- ( ph -> F : ( R X. S ) --> C ) |
|
fovcdmd.2 | |- ( ph -> A e. R ) |
||
fovcdmd.3 | |- ( ph -> B e. S ) |
||
Assertion | fovcdmd | |- ( ph -> ( A F B ) e. C ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fovcdmd.1 | |- ( ph -> F : ( R X. S ) --> C ) |
|
2 | fovcdmd.2 | |- ( ph -> A e. R ) |
|
3 | fovcdmd.3 | |- ( ph -> B e. S ) |
|
4 | fovcdm | |- ( ( F : ( R X. S ) --> C /\ A e. R /\ B e. S ) -> ( A F B ) e. C ) |
|
5 | 1 2 3 4 | syl3anc | |- ( ph -> ( A F B ) e. C ) |