Definition df-recs 8357

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 8396 for more details on why this definition is desirable. Unlike df-rdg 8396 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 8389 and recsval 8390 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 8356	. 2 class recs(𝐹)
3		con0 6360	. . 3 class On
4		cep 5560	. . 3 class E
5	3, 4, 1	cwrecs 8307	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1568	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8358  recseq  8359  nfrecs  8360  tfrlem6  8367  tfr1ALT  8386  tfr2ALT  8387  tfr3ALT  8388  csbrecsg  37918