Definition df-recs 8303

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 8341 for more details on why this definition is desirable. Unlike df-rdg 8341 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 8334 and recsval 8335 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 8302	. 2 class recs(𝐹)
3		con0 6317	. . 3 class On
4		cep 5523	. . 3 class E
5	3, 4, 1	cwrecs 8253	. 2 class wrecs( E , On, 𝐹)
6	2, 5	wceq 1541	1 wff recs(𝐹) = wrecs( E , On, 𝐹)

This definition is referenced by:  dfrecs3  8304  recseq  8305  nfrecs  8306  tfr1ALT  8331  tfr2ALT  8332  tfr3ALT  8333  csbrecsg  37533