Definition df-recs 8356

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 8395 for more details on why this definition is desirable. Unlike df-rdg 8395 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 8388 and recsval 8389 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 8355	. 2 class recs(𝐹)
3		con0 6360	. . 3 class On
4		cep 5559	. . 3 class E
5	3, 4, 1	cwrecs 8306	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1569	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is used by:  dfrecs3  8357  recseq  8358  nfrecs  8359  tfrlem6  8366  tfr1ALT  8385  tfr2ALT  8386  tfr3ALT  8387  csbrecsg  38002