Definition df-recs 8409

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 8448 for more details on why this definition is desirable. Unlike df-rdg 8448 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 8441 and recsval 8442 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 8408	. 2 class recs(𝐹)
3		con0 6385	. . 3 class On
4		cep 5587	. . 3 class E
5	3, 4, 1	cwrecs 8334	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1536	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8410  dfrecs3OLD  8411  recseq  8412  nfrecs  8413  tfr1ALT  8438  tfr2ALT  8439  tfr3ALT  8440  csbrecsg  37310