Definition df-recs 8404

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 8443 for more details on why this definition is desirable. Unlike df-rdg 8443 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 8436 and recsval 8437 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 8403	. 2 class recs(𝐹)
3		con0 6377	. . 3 class On
4		cep 5554	. . 3 class E
5	3, 4, 1	cwrecs 8354	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1570	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is used by:  dfrecs3  8405  recseq  8406  nfrecs  8407  tfrlem6  8414  tfr1ALT  8433  tfr2ALT  8434  tfr3ALT  8435  csbrecsg  38442