Definition df-recs 8411

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 8450 for more details on why this definition is desirable. Unlike df-rdg 8450 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 8443 and recsval 8444 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 8410	. 2 class recs(𝐹)
3		con0 6384	. . 3 class On
4		cep 5583	. . 3 class E
5	3, 4, 1	cwrecs 8336	. 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  8412  dfrecs3OLD  8413  recseq  8414  nfrecs  8415  tfr1ALT  8440  tfr2ALT  8441  tfr3ALT  8442  csbrecsg  37329