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 | ||
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Hypotheses | nfwrecs.1 | |- F/_ x R |
|
nfwrecs.2 | |- F/_ x A |
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nfwrecs.3 | |- F/_ x F |
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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 |
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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 ) |