Definition df-recs 8366

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 8405 for more details on why this definition is desirable. Unlike df-rdg 8405 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 8398 and recsval 8399 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 8365	. 2 class recs(𝐹)
3		con0 6361	. . 3 class On
4		cep 5578	. . 3 class E
5	3, 4, 1	cwrecs 8291	. 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  8367  dfrecs3OLD  8368  recseq  8369  nfrecs  8370  tfr1ALT  8395  tfr2ALT  8396  tfr3ALT  8397  csbrecsg  36147