Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-rank Unicode version

Definition df-rank 7680
 Description: Define the rank function. See rankval 7731, rankval2 7733, rankval3 7755, or rankval4 7782 its value. The rank is a kind of "inverse" of the cumulative hierarchy of sets function : given a set, it returns an ordinal number telling us the smallest layer of the hierarchy to which the set belongs. Based on Definition 9.14 of [TakeutiZaring] p. 79. Theorem rankid 7748 illustrates the "inverse" concept. Another nice theorem showing the relationship is rankr1a 7751. (Contributed by NM, 11-Oct-2003.)
Assertion
Ref Expression
df-rank
Distinct variable group:   ,

Detailed syntax breakdown of Definition df-rank
StepHypRef Expression
1 crnk 7678 . 2
2 vx . . 3
3 cvv 2948 . . 3
42cv 1651 . . . . . 6
5 vy . . . . . . . . 9
65cv 1651 . . . . . . . 8
76csuc 4575 . . . . . . 7
8 cr1 7677 . . . . . . 7
97, 8cfv 5445 . . . . . 6
104, 9wcel 1725 . . . . 5
11 con0 4573 . . . . 5
1210, 5, 11crab 2701 . . . 4
1312cint 4042 . . 3
142, 3, 13cmpt 4258 . 2
151, 14wceq 1652 1
 Colors of variables: wff set class This definition is referenced by:  rankf  7709  rankvalb  7712
 Copyright terms: Public domain W3C validator