Definition df-recs 8173

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 8212 for more details on why this definition is desirable. Unlike df-rdg 8212 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 8205 and recsval 8206 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 8172	. 2 class recs(𝐹)
3		con0 6251	. . 3 class On
4		cep 5485	. . 3 class E
5	3, 4, 1	cwrecs 8098	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1539	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8174  dfrecs3OLD  8175  recseq  8176  nfrecs  8177  tfr1ALT  8202  tfr2ALT  8203  tfr3ALT  8204  csbrecsg  35426