Definition df-recs 8008

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 8046 for more details on why this definition is desirable. Unlike df-rdg 8046 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 8039 and recsval 8040 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 8007	. 2 class recs(𝐹)
3		con0 6191	. . 3 class On
4		cep 5464	. . 3 class E
5	3, 4, 1	cwrecs 7946	. 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  8009  recseq  8010  nfrecs  8011  tfr1ALT  8036  tfr2ALT  8037  tfr3ALT  8038  csbrecsg  34612