Definition df-recs 8427

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 8466 for more details on why this definition is desirable. Unlike df-rdg 8466 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 8459 and recsval 8460 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 8426	. 2 class recs(𝐹)
3		con0 6395	. . 3 class On
4		cep 5598	. . 3 class E
5	3, 4, 1	cwrecs 8352	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1537	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8428  dfrecs3OLD  8429  recseq  8430  nfrecs  8431  tfr1ALT  8456  tfr2ALT  8457  tfr3ALT  8458  csbrecsg  37294