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Definition df-recs 8411
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 8450 for more details on why this definition is desirable. Unlike df-rdg 8450 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 8443 and recsval 8444 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 8410 . 2 class recs(𝐹)
3 con0 6384 . . 3 class On
4 cep 5583 . . 3 class E
53, 4, 1cwrecs 8336 . 2 class wrecs( E , On, 𝐹)
62, 5wceq 1540 1 wff recs(𝐹) = wrecs( E , On, 𝐹)
Colors of variables: wff setvar class
This definition is referenced by:  dfrecs3  8412  dfrecs3OLD  8413  recseq  8414  nfrecs  8415  tfr1ALT  8440  tfr2ALT  8441  tfr3ALT  8442  csbrecsg  37329
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