Definition df-recs 7707

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 7745 for more details on why this definition is desirable. Unlike df-rdg 7745 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 7738 and recsval 7739 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 7706	. 2 class recs(𝐹)
3		con0 5943	. . 3 class On
4		cep 5230	. . 3 class E
5	3, 4, 1	cwrecs 7644	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1637	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  7708  recseq  7709  nfrecs  7710  tfr1ALT  7735  tfr2ALT  7736  tfr3ALT  7737  csbrecsg  33493