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Definition df-iota 5024
 Description: Define Russell's definition description binder, which can be read as "the unique such that ," where ordinarily contains as a free variable. Our definition is meaningful only when there is exactly one such that is true (see iotaval 5035); otherwise, it evaluates to the empty set (see iotanul 5039). Russell used the inverted iota symbol to represent the binder. Sometimes proofs need to expand an iota-based definition. That is, given "X = the x for which ... x ... x ..." holds, the proof needs to get to "... X ... X ...". A general strategy to do this is to use iotacl 5047 (for unbounded iota). This can be easier than applying a version that applies an explicit substitution, because substituting an iota into its own property always has a bound variable clash which must be first renamed or else guarded with NF. (Contributed by Andrew Salmon, 30-Jun-2011.)
Assertion
Ref Expression
df-iota
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Detailed syntax breakdown of Definition df-iota
StepHypRef Expression
1 wph . . 3
2 vx . . 3
31, 2cio 5022 . 2
41, 2cab 2086 . . . . 5
5 vy . . . . . . 7
65cv 1298 . . . . . 6
76csn 3474 . . . . 5
84, 7wceq 1299 . . . 4
98, 5cab 2086 . . 3
109cuni 3683 . 2
113, 10wceq 1299 1
 Colors of variables: wff set class This definition is referenced by:  dfiota2  5025  iotaeq  5032  iotabi  5033  iotass  5041  dffv4g  5350  nfvres  5386
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