Definition df-recs 8211

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 8250 for more details on why this definition is desirable. Unlike df-rdg 8250 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 8243 and recsval 8244 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 8210	. 2 class recs(𝐹)
3		con0 6270	. . 3 class On
4		cep 5495	. . 3 class E
5	3, 4, 1	cwrecs 8136	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1539	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8212  dfrecs3OLD  8213  recseq  8214  nfrecs  8215  tfr1ALT  8240  tfr2ALT  8241  tfr3ALT  8242  csbrecsg  35508