Definition df-recs 7810

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 7848 for more details on why this definition is desirable. Unlike df-rdg 7848 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 7841 and recsval 7842 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 7809	. 2 class recs(𝐹)
3		con0 6026	. . 3 class On
4		cep 5312	. . 3 class E
5	3, 4, 1	cwrecs 7747	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1508	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  7811  recseq  7812  nfrecs  7813  tfr1ALT  7838  tfr2ALT  7839  tfr3ALT  7840  csbrecsg  34088