Description: Bound-variable hypothesis builder for function value, analogous to nffv . To prove a deduction version of this analogous to nffvd is not easily possible because a deduction version of nfdfat cannot be shown easily. (Contributed by Alexander van der Vekens, 26-May-2017)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | nfafv.1 | |- F/_ x F |
|
| nfafv.2 | |- F/_ x A |
||
| Assertion | nfafv | |- F/_ x ( F ''' A ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfafv.1 | |- F/_ x F |
|
| 2 | nfafv.2 | |- F/_ x A |
|
| 3 | dfafv2 | |- ( F ''' A ) = if ( F defAt A , ( F ` A ) , _V ) |
|
| 4 | 1 2 | nfdfat | |- F/ x F defAt A |
| 5 | 1 2 | nffv | |- F/_ x ( F ` A ) |
| 6 | nfcv | |- F/_ x _V |
|
| 7 | 4 5 6 | nfif | |- F/_ x if ( F defAt A , ( F ` A ) , _V ) |
| 8 | 3 7 | nfcxfr | |- F/_ x ( F ''' A ) |