Definition df-recs 8300

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 8338 for more details on why this definition is desirable. Unlike df-rdg 8338 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 8331 and recsval 8332 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 8299	. 2 class recs(𝐹)
3		con0 6312	. . 3 class On
4		cep 5519	. . 3 class E
5	3, 4, 1	cwrecs 8250	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1542	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8301  recseq  8302  nfrecs  8303  tfr1ALT  8328  tfr2ALT  8329  tfr3ALT  8330  csbrecsg  37632