Definition df-recs 8308

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 8346 for more details on why this definition is desirable. Unlike df-rdg 8346 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 8339 and recsval 8340 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 8307	. 2 class recs(𝐹)
3		con0 6321	. . 3 class On
4		cep 5527	. . 3 class E
5	3, 4, 1	cwrecs 8258	. 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  8309  recseq  8310  nfrecs  8311  tfr1ALT  8336  tfr2ALT  8337  tfr3ALT  8338  csbrecsg  37641