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Definition df-recs 7332
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 7370 for more details on why this definition is desirable. Unlike df-rdg 7370 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 7363 and recsval 7364 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 7331 . 2 class recs(𝐹)
3 con0 5625 . . 3 class On
4 cep 4936 . . 3 class E
53, 4, 1cwrecs 7270 . 2 class wrecs( E , On, 𝐹)
62, 5wceq 1474 1 wff recs(𝐹) = wrecs( E , On, 𝐹)
Colors of variables: wff setvar class
This definition is referenced by:  dfrecs3  7333  recseq  7334  nfrecs  7335  tfr1ALT  7360  tfr2ALT  7361  tfr3ALT  7362  csbrecsg  32133
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