Definition df-recs 8301

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 8339 for more details on why this definition is desirable. Unlike df-rdg 8339 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 8332 and recsval 8333 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 8300	. 2 class recs(𝐹)
3		con0 6311	. . 3 class On
4		cep 5522	. . 3 class E
5	3, 4, 1	cwrecs 8251	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1540	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8302  recseq  8303  nfrecs  8304  tfr1ALT  8329  tfr2ALT  8330  tfr3ALT  8331  csbrecsg  37301