Definition df-recs 7468

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 7506 for more details on why this definition is desirable. Unlike df-rdg 7506 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 7499 and recsval 7500 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 7467	. 2 class recs(𝐹)
3		con0 5723	. . 3 class On
4		cep 5028	. . 3 class E
5	3, 4, 1	cwrecs 7406	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1483	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  7469  recseq  7470  nfrecs  7471  tfr1ALT  7496  tfr2ALT  7497  tfr3ALT  7498  csbrecsg  33174