Definition df-recs 8379

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 8418 for more details on why this definition is desirable. Unlike df-rdg 8418 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 8411 and recsval 8412 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 8378	. 2 class recs(𝐹)
3		con0 6362	. . 3 class On
4		cep 5549	. . 3 class E
5	3, 4, 1	cwrecs 8329	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1569	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is used by:  dfrecs3  8380  recseq  8381  nfrecs  8382  tfrlem6  8389  tfr1ALT  8408  tfr2ALT  8409  tfr3ALT  8410  csbrecsg  38294