Definition df-recs 8363

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 8402 for more details on why this definition is desirable. Unlike df-rdg 8402 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 8395 and recsval 8396 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 8362	. 2 class recs(𝐹)
3		con0 6361	. . 3 class On
4		cep 5558	. . 3 class E
5	3, 4, 1	cwrecs 8313	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1570	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is used by:  dfrecs3  8364  recseq  8365  nfrecs  8366  tfrlem6  8373  tfr1ALT  8392  tfr2ALT  8393  tfr3ALT  8394  csbrecsg  38069