Definition df-recs 8368

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 8407 for more details on why this definition is desirable. Unlike df-rdg 8407 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 8400 and recsval 8401 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 8367	. 2 class recs(𝐹)
3		con0 6362	. . 3 class On
4		cep 5579	. . 3 class E
5	3, 4, 1	cwrecs 8293	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1542	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8369  dfrecs3OLD  8370  recseq  8371  nfrecs  8372  tfr1ALT  8397  tfr2ALT  8398  tfr3ALT  8399  csbrecsg  36198