Definition df-recs 8401

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 8440 for more details on why this definition is desirable. Unlike df-rdg 8440 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 8433 and recsval 8434 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 8400	. 2 class recs(𝐹)
3		con0 6376	. . 3 class On
4		cep 5585	. . 3 class E
5	3, 4, 1	cwrecs 8326	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1534	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8402  dfrecs3OLD  8403  recseq  8404  nfrecs  8405  tfr1ALT  8430  tfr2ALT  8431  tfr3ALT  8432  csbrecsg  37035