Definition df-recs 8383

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 8422 for more details on why this definition is desirable. Unlike df-rdg 8422 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 8415 and recsval 8416 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 8382	. 2 class recs(𝐹)
3		con0 6352	. . 3 class On
4		cep 5552	. . 3 class E
5	3, 4, 1	cwrecs 8308	. 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  8384  dfrecs3OLD  8385  recseq  8386  nfrecs  8387  tfr1ALT  8412  tfr2ALT  8413  tfr3ALT  8414  csbrecsg  37292