Definition df-recs 8340

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 8378 for more details on why this definition is desirable. Unlike df-rdg 8378 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 8371 and recsval 8372 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 8339	. 2 class recs(𝐹)
3		con0 6332	. . 3 class On
4		cep 5537	. . 3 class E
5	3, 4, 1	cwrecs 8290	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1540	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8341  recseq  8342  nfrecs  8343  tfr1ALT  8368  tfr2ALT  8369  tfr3ALT  8370  csbrecsg  37316