Definition df-recs 8343

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 8381 for more details on why this definition is desirable. Unlike df-rdg 8381 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 8374 and recsval 8375 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 8342	. 2 class recs(𝐹)
3		con0 6335	. . 3 class On
4		cep 5540	. . 3 class E
5	3, 4, 1	cwrecs 8293	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1540	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8344  recseq  8345  nfrecs  8346  tfr1ALT  8371  tfr2ALT  8372  tfr3ALT  8373  csbrecsg  37323