Description: Obsolete proof of fnresi as of 27-Dec-2023. (Contributed by NM, 27-Aug-2004) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | fnresiOLD | |- ( _I |` A ) Fn A |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | funi | |- Fun _I |
|
| 2 | funres | |- ( Fun _I -> Fun ( _I |` A ) ) |
|
| 3 | 1 2 | ax-mp | |- Fun ( _I |` A ) |
| 4 | dmresi | |- dom ( _I |` A ) = A |
|
| 5 | df-fn | |- ( ( _I |` A ) Fn A <-> ( Fun ( _I |` A ) /\ dom ( _I |` A ) = A ) ) |
|
| 6 | 3 4 5 | mpbir2an | |- ( _I |` A ) Fn A |