Definition df-recs 8364

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 8403 for more details on why this definition is desirable. Unlike df-rdg 8403 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 8396 and recsval 8397 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

Step	Hyp	Ref	Expression
1		cF	. . 3 class 𝐹
2	1	crecs 8363	. 2 class recs(𝐹)
3		con0 6361	. . 3 class On
4		cep 5558	. . 3 class E
5	3, 4, 1	cwrecs 8314	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1570	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is used by:  dfrecs3  8365  recseq  8366  nfrecs  8367  tfrlem6  8374  tfr1ALT  8393  tfr2ALT  8394  tfr3ALT  8395  csbrecsg  38090