Description: Bound-variable hypothesis builder for a function. (Contributed by NM, 30-Jan-2004)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | nffun.1 | |- F/_ x F |
|
| Assertion | nffun | |- F/ x Fun F |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nffun.1 | |- F/_ x F |
|
| 2 | df-fun | |- ( Fun F <-> ( Rel F /\ ( F o. `' F ) C_ _I ) ) |
|
| 3 | 1 | nfrel | |- F/ x Rel F |
| 4 | 1 | nfcnv | |- F/_ x `' F |
| 5 | 1 4 | nfco | |- F/_ x ( F o. `' F ) |
| 6 | nfcv | |- F/_ x _I |
|
| 7 | 5 6 | nfss | |- F/ x ( F o. `' F ) C_ _I |
| 8 | 3 7 | nfan | |- F/ x ( Rel F /\ ( F o. `' F ) C_ _I ) |
| 9 | 2 8 | nfxfr | |- F/ x Fun F |