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Metamath Proof Explorer

Definition df-recs

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 for more details on why this definition is desirable. Unlike df-rdg 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 and recsval for the primary contract of this definition. (Contributed by Stefan O'Rear, 18-Jan-2015) (Revised by Scott Fenton, 3-Aug-2020)

		Ref	Expression
	Assertion	df-recs	$⊢ recs (F) = wrecs (E, On, F)$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cF	$class F$
1	0	crecs	$class recs (F)$
2		cep	$class E$
3		con0	$class On$
4	3 2 0	cwrecs	$class wrecs (E, On, F)$
5	1 4	wceq	$wff recs (F) = wrecs (E, On, F)$