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Definition df-fv 4853
Description: Define the value of a function,  F ` , also known as function application. For example,  _I  `  (/)  (/). Typically, function  F is defined using maps-to notation (see df-mpt 3811), but this is not required. For example, F = {  <. 2 , 6  >.,  <. 3 , 9  >. } -> ( F  ` 3 ) = 9 . We will later define two-argument functions using ordered pairs as  F  F `  <. ,  >.. This particular definition is quite convenient: it can be applied to any class and evaluates to the empty set when it is not meaningful. The left apostrophe notation originated with Peano and was adopted in Definition *30.01 of [WhiteheadRussell] p. 235, Definition 10.11 of [Quine] p. 68, and Definition 6.11 of [TakeutiZaring] p. 26. It means the same thing as the more familiar  F notation for a function's value at , i.e. " F of ," but without context-dependent notational ambiguity. (Contributed by NM, 1-Aug-1994.) Revised to use  iota. (Revised by Scott Fenton, 6-Oct-2017.)
Assertion
Ref Expression
df-fv  F `
 iota F
Distinct variable groups:   ,   , F

Detailed syntax breakdown of Definition df-fv
StepHypRef Expression
1 cA . . 3
2 cF . . 3  F
31, 2cfv 4845 . 2  F `
4 vx . . . . 5  setvar
54cv 1241 . . . 4
61, 5, 2wbr 3755 . . 3  F
76, 4cio 4808 . 2  iota F
83, 7wceq 1242 1  F `  iota F
Colors of variables: wff set class
This definition is referenced by:  tz6.12-2  5112  fveu  5113  fv2  5116  dffv3g  5117  fveq1  5120  fveq2  5121  nffv  5128  fvss  5132  funfvex  5135  fvres  5141  tz6.12-1  5143  nfvres  5149  0fv  5151  csbfv12g  5152  ovtposg  5815
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