Definition df-recs 7428

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 7466 for more details on why this definition is desirable. Unlike df-rdg 7466 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 7459 and recsval 7460 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 7427	. 2 class recs(𝐹)
3		con0 5692	. . 3 class On
4		cep 4993	. . 3 class E
5	3, 4, 1	cwrecs 7366	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1480	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  7429  recseq  7430  nfrecs  7431  tfr1ALT  7456  tfr2ALT  7457  tfr3ALT  7458  csbrecsg  32845