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Definition df-recs 7999
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 8037 for more details on why this definition is desirable. Unlike df-rdg 8037 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 8030 and recsval 8031 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 7998 . 2 class recs(𝐹)
3 con0 6185 . . 3 class On
4 cep 5458 . . 3 class E
53, 4, 1cwrecs 7937 . 2 class wrecs( E , On, 𝐹)
62, 5wceq 1528 1 wff recs(𝐹) = wrecs( E , On, 𝐹)
Colors of variables: wff setvar class
This definition is referenced by:  dfrecs3  8000  recseq  8001  nfrecs  8002  tfr1ALT  8027  tfr2ALT  8028  tfr3ALT  8029  csbrecsg  34492
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