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Definition df-oprab 5543
 Description: Define the class abstraction (class builder) of a collection of nested ordered pairs (for use in defining operations). This is a special case of Definition 4.16 of [TakeutiZaring] p. 14. Normally , , and are distinct, although the definition doesn't strictly require it. See df-ov 5542 for the value of an operation. The brace notation is called "class abstraction" by Quine; it is also called a "class builder" in the literature. The value of the most common operation class builder is given by ovmpt2 5663. (Contributed by NM, 12-Mar-1995.)
Assertion
Ref Expression
df-oprab
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,)

Detailed syntax breakdown of Definition df-oprab
StepHypRef Expression
1 wph . . 3
2 vx . . 3
3 vy . . 3
4 vz . . 3
51, 2, 3, 4coprab 5540 . 2
6 vw . . . . . . . . 9
76cv 1258 . . . . . . . 8
82cv 1258 . . . . . . . . . 10
93cv 1258 . . . . . . . . . 10
108, 9cop 3405 . . . . . . . . 9
114cv 1258 . . . . . . . . 9
1210, 11cop 3405 . . . . . . . 8
137, 12wceq 1259 . . . . . . 7
1413, 1wa 101 . . . . . 6
1514, 4wex 1397 . . . . 5
1615, 3wex 1397 . . . 4
1716, 2wex 1397 . . 3
1817, 6cab 2042 . 2
195, 18wceq 1259 1
 Colors of variables: wff set class This definition is referenced by:  oprabid  5564  dfoprab2  5579  nfoprab1  5581  nfoprab2  5582  nfoprab3  5583  nfoprab  5584  oprabbid  5585  ssoprab2  5588  mpt20  5601  cbvoprab2  5604  eloprabga  5618  oprabrexex2  5784  eloprabi  5849  cnvoprab  5882  dftpos3  5907
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