Description: The intersection with a function is a function. Exercise 14(a) of Enderton p. 53. (Contributed by NM, 19-Mar-2004) (Proof shortened by Andrew Salmon, 17-Sep-2011)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | funin | |- ( Fun F -> Fun ( F i^i G ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | inss1 | |- ( F i^i G ) C_ F |
|
| 2 | funss | |- ( ( F i^i G ) C_ F -> ( Fun F -> Fun ( F i^i G ) ) ) |
|
| 3 | 1 2 | ax-mp | |- ( Fun F -> Fun ( F i^i G ) ) |