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Definition df-recs 8398
Description: Define a function recs(𝐹) on On, the class of ordinal numbers, by transfinite recursion given a rule 𝐹 which sets the next value given all values so far. See df-rdg 8437 for more details on why this definition is desirable. Unlike df-rdg 8437 which restricts the update rule to use only the previous value, this version allows the update rule to use all previous values, which is why it is described as "strong", although it is actually more primitive. See recsfnon 8430 and recsval 8431 for the primary contract of this definition. (Contributed by Stefan O'Rear, 18-Jan-2015.) (Revised by Scott Fenton, 3-Aug-2020.)
Assertion
Ref Expression
df-recs recs(𝐹) = wrecs( E , On, 𝐹)

Detailed syntax breakdown of Definition df-recs
StepHypRef Expression
1 cF . . 3 class 𝐹
21crecs 8397 . 2 class recs(𝐹)
3 con0 6374 . . 3 class On
4 cep 5585 . . 3 class E
53, 4, 1cwrecs 8323 . 2 class wrecs( E , On, 𝐹)
62, 5wceq 1533 1 wff recs(𝐹) = wrecs( E , On, 𝐹)
Colors of variables: wff setvar class
This definition is referenced by:  dfrecs3  8399  dfrecs3OLD  8400  recseq  8401  nfrecs  8402  tfr1ALT  8427  tfr2ALT  8428  tfr3ALT  8429  csbrecsg  36840
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