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Definition df-fv 4940
 Description: Define the value of a function, (𝐹‘𝐴), also known as function application. For example, ( I ‘∅) = ∅. Typically, function 𝐹 is defined using maps-to notation (see df-mpt 3849), 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 (𝐴𝐹𝐵) = (𝐹‘⟨𝐴, 𝐵⟩). 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(𝐴) notation for a function's value at 𝐴, i.e. "𝐹 of 𝐴," but without context-dependent notational ambiguity. (Contributed by NM, 1-Aug-1994.) Revised to use ℩. (Revised by Scott Fenton, 6-Oct-2017.)
Assertion
Ref Expression
df-fv (𝐹𝐴) = (℩𝑥𝐴𝐹𝑥)
Distinct variable groups:   𝑥,𝐴   𝑥,𝐹

Detailed syntax breakdown of Definition df-fv
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cF . . 3 class 𝐹
31, 2cfv 4932 . 2 class (𝐹𝐴)
4 vx . . . . 5 setvar 𝑥
54cv 1284 . . . 4 class 𝑥
61, 5, 2wbr 3793 . . 3 wff 𝐴𝐹𝑥
76, 4cio 4895 . 2 class (℩𝑥𝐴𝐹𝑥)
83, 7wceq 1285 1 wff (𝐹𝐴) = (℩𝑥𝐴𝐹𝑥)
 Colors of variables: wff set class This definition is referenced by:  tz6.12-2  5200  fveu  5201  fv2  5204  dffv3g  5205  fveq1  5208  fveq2  5209  nffv  5216  fvss  5220  funfvex  5223  fvres  5230  tz6.12-1  5232  nfvres  5238  0fv  5240  csbfv12g  5241  ovtposg  5908
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