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Definition df-recs 7355
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 7393 for more details on why this definition is desirable. Unlike df-rdg 7393 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 7386 and recsval 7387 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 7354 . 2 class recs(𝐹)
3 con0 5640 . . 3 class On
4 cep 4947 . . 3 class E
53, 4, 1cwrecs 7293 . 2 class wrecs( E , On, 𝐹)
62, 5wceq 1475 1 wff recs(𝐹) = wrecs( E , On, 𝐹)
Colors of variables: wff setvar class
This definition is referenced by:  dfrecs3  7356  recseq  7357  nfrecs  7358  tfr1ALT  7383  tfr2ALT  7384  tfr3ALT  7385  csbrecsg  32350
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