Definition df-recs 8369

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 8408 for more details on why this definition is desirable. Unlike df-rdg 8408 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 8401 and recsval 8402 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 8368	. 2 class recs(𝐹)
3		con0 6357	. . 3 class On
4		cep 5572	. . 3 class E
5	3, 4, 1	cwrecs 8294	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1533	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8370  dfrecs3OLD  8371  recseq  8372  nfrecs  8373  tfr1ALT  8398  tfr2ALT  8399  tfr3ALT  8400  csbrecsg  36715