Definition df-recs 8304

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 8343 for more details on why this definition is desirable. Unlike df-rdg 8343 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 8336 and recsval 8337 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 8303	. 2 class recs(𝐹)
3		con0 6313	. . 3 class On
4		cep 5519	. . 3 class E
5	3, 4, 1	cwrecs 8254	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1548	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8305  recseq  8306  nfrecs  8307  tfrlem6  8314  tfr1ALT  8333  tfr2ALT  8334  tfr3ALT  8335  csbrecsg  37703