Description: Bound-variable hypothesis builder for the well-ordered recursive function generator. (Contributed by Scott Fenton, 9-Jun-2018) (Proof shortened by Scott Fenton, 17-Nov-2024)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | nfwrecs.1 | |- F/_ x R |
|
| nfwrecs.2 | |- F/_ x A |
||
| nfwrecs.3 | |- F/_ x F |
||
| Assertion | nfwrecs | |- F/_ x wrecs ( R , A , F ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfwrecs.1 | |- F/_ x R |
|
| 2 | nfwrecs.2 | |- F/_ x A |
|
| 3 | nfwrecs.3 | |- F/_ x F |
|
| 4 | df-wrecs | |- wrecs ( R , A , F ) = frecs ( R , A , ( F o. 2nd ) ) |
|
| 5 | nfcv | |- F/_ x 2nd |
|
| 6 | 3 5 | nfco | |- F/_ x ( F o. 2nd ) |
| 7 | 1 2 6 | nffrecs | |- F/_ x frecs ( R , A , ( F o. 2nd ) ) |
| 8 | 4 7 | nfcxfr | |- F/_ x wrecs ( R , A , F ) |