Definition df-recs 8086

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 8124 for more details on why this definition is desirable. Unlike df-rdg 8124 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 8117 and recsval 8118 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 8085	. 2 class recs(𝐹)
3		con0 6191	. . 3 class On
4		cep 5444	. . 3 class E
5	3, 4, 1	cwrecs 8024	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1543	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8087  recseq  8088  nfrecs  8089  tfr1ALT  8114  tfr2ALT  8115  tfr3ALT  8116  csbrecsg  35185