Definition df-recs 8315

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 8353 for more details on why this definition is desirable. Unlike df-rdg 8353 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 8346 and recsval 8347 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 8314	. 2 class recs(𝐹)
3		con0 6327	. . 3 class On
4		cep 5533	. . 3 class E
5	3, 4, 1	cwrecs 8265	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1542	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8316  recseq  8317  nfrecs  8318  tfr1ALT  8343  tfr2ALT  8344  tfr3ALT  8345  csbrecsg  37610