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 ) |