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Definition df-iota 4790
 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 4801); otherwise, it evaluates to the empty set (see iotanul 4805). 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 4813 (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 4788 . 2
41, 2cab 2004 . . . . 5
5 vy . . . . . . 7
65cv 1225 . . . . . 6
76csn 3346 . . . . 5
84, 7wceq 1226 . . . 4
98, 5cab 2004 . . 3
109cuni 3550 . 2
113, 10wceq 1226 1
 Colors of variables: wff set class This definition is referenced by:  dfiota2  4791  iotaeq  4798  iotabi  4799  iotass  4807  dffv4g  5096  nfvres  5127
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