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Definition df-fv 4825
Description: Define the value of a function, (𝐹A), also known as function application. For example, ( I ‘∅) = ∅. Typically, function 𝐹 is defined using maps-to notation (see df-mpt 3783), 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 4817 . 2 class (𝐹A)
4 vx . . . . 5 setvar x
54cv 1222 . . . 4 class x
61, 5, 2wbr 3727 . . 3 wff A𝐹x
76, 4cio 4780 . 2 class (℩xA𝐹x)
83, 7wceq 1223 1 wff (𝐹A) = (℩xA𝐹x)
Colors of variables: wff set class
This definition is referenced by:  tz6.12-2  5082  fveu  5083  fv2  5086  dffv3g  5087  fveq1  5090  fveq2  5091  nffv  5098  fvss  5102  funfvex  5105  fvres  5111  tz6.12-1  5113  nfvres  5119  0fv  5121  csbfv12g  5122  ovtposg  5784
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