Definition df-recs 8291

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 8329 for more details on why this definition is desirable. Unlike df-rdg 8329 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 8322 and recsval 8323 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 8290	. 2 class recs(𝐹)
3		con0 6306	. . 3 class On
4		cep 5515	. . 3 class E
5	3, 4, 1	cwrecs 8241	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1541	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8292  recseq  8293  nfrecs  8294  tfr1ALT  8319  tfr2ALT  8320  tfr3ALT  8321  csbrecsg  37361