Definition df-recs 8297

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 8335 for more details on why this definition is desirable. Unlike df-rdg 8335 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 8328 and recsval 8329 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 8296	. 2 class recs(𝐹)
3		con0 6311	. . 3 class On
4		cep 5518	. . 3 class E
5	3, 4, 1	cwrecs 8247	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1541	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8298  recseq  8299  nfrecs  8300  tfr1ALT  8325  tfr2ALT  8326  tfr3ALT  8327  csbrecsg  37393