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 | ⊢ Ⅎ 𝑥 𝑅 | |
nfwrecs.2 | ⊢ Ⅎ 𝑥 𝐴 | ||
nfwrecs.3 | ⊢ Ⅎ 𝑥 𝐹 | ||
Assertion | nfwrecs | ⊢ Ⅎ 𝑥 wrecs ( 𝑅 , 𝐴 , 𝐹 ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfwrecs.1 | ⊢ Ⅎ 𝑥 𝑅 | |
2 | nfwrecs.2 | ⊢ Ⅎ 𝑥 𝐴 | |
3 | nfwrecs.3 | ⊢ Ⅎ 𝑥 𝐹 | |
4 | df-wrecs | ⊢ wrecs ( 𝑅 , 𝐴 , 𝐹 ) = frecs ( 𝑅 , 𝐴 , ( 𝐹 ∘ 2nd ) ) | |
5 | nfcv | ⊢ Ⅎ 𝑥 2nd | |
6 | 3 5 | nfco | ⊢ Ⅎ 𝑥 ( 𝐹 ∘ 2nd ) |
7 | 1 2 6 | nffrecs | ⊢ Ⅎ 𝑥 frecs ( 𝑅 , 𝐴 , ( 𝐹 ∘ 2nd ) ) |
8 | 4 7 | nfcxfr | ⊢ Ⅎ 𝑥 wrecs ( 𝑅 , 𝐴 , 𝐹 ) |