Definition df-recs 7635

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 7673 for more details on why this definition is desirable. Unlike df-rdg 7673 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 7666 and recsval 7667 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 7634	. 2 class recs(𝐹)
3		con0 5882	. . 3 class On
4		cep 5176	. . 3 class E
5	3, 4, 1	cwrecs 7573	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1630	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  7636  recseq  7637  nfrecs  7638  tfr1ALT  7663  tfr2ALT  7664  tfr3ALT  7665  csbrecsg  33483