Definition df-recs 8344

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 8383 for more details on why this definition is desirable. Unlike df-rdg 8383 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 8376 and recsval 8377 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 8343	. 2 class recs(𝐹)
3		con0 6348	. . 3 class On
4		cep 5548	. . 3 class E
5	3, 4, 1	cwrecs 8294	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1562	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8345  recseq  8346  nfrecs  8347  tfrlem6  8354  tfr1ALT  8373  tfr2ALT  8374  tfr3ALT  8375  csbrecsg  37827