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Definition df-afv 41727
Description: Alternative definition of the value of a function, (𝐹'''𝐴), also known as function application. In contrast to (𝐹𝐴) = ∅ (see df-fv 6119 and ndmfv 6448), (𝐹'''𝐴) = V if F is not defined for A! (Contributed by Alexander van der Vekens, 25-May-2017.) (Revised by BJ/AV, 25-Aug-2022.)
Assertion
Ref Expression
df-afv (𝐹'''𝐴) = (℩'𝑥𝐴𝐹𝑥)
Distinct variable groups:   𝑥,𝐴   𝑥,𝐹

Detailed syntax breakdown of Definition df-afv
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cF . . 3 class 𝐹
31, 2cafv 41724 . 2 class (𝐹'''𝐴)
4 vx . . . . 5 setvar 𝑥
54cv 1636 . . . 4 class 𝑥
61, 5, 2wbr 4855 . . 3 wff 𝐴𝐹𝑥
76, 4caiota 41685 . 2 class (℩'𝑥𝐴𝐹𝑥)
83, 7wceq 1637 1 wff (𝐹'''𝐴) = (℩'𝑥𝐴𝐹𝑥)
Colors of variables: wff setvar class
This definition is referenced by:  dfafv2  41739
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