Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-afv | Structured version Visualization version GIF version |
Description: Alternative definition of the value of a function, (𝐹'''𝐴), also known as function application. In contrast to (𝐹‘𝐴) = ∅ (see df-fv 5812 and ndmfv 6128), (𝐹'''𝐴) = V if F is not defined for A! (Contributed by Alexander van der Vekens, 25-May-2017.) |
Ref | Expression |
---|---|
df-afv | ⊢ (𝐹'''𝐴) = if(𝐹 defAt 𝐴, (℩𝑥𝐴𝐹𝑥), V) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class 𝐴 | |
2 | cF | . . 3 class 𝐹 | |
3 | 1, 2 | cafv 39843 | . 2 class (𝐹'''𝐴) |
4 | 1, 2 | wdfat 39842 | . . 3 wff 𝐹 defAt 𝐴 |
5 | vx | . . . . . 6 setvar 𝑥 | |
6 | 5 | cv 1474 | . . . . 5 class 𝑥 |
7 | 1, 6, 2 | wbr 4583 | . . . 4 wff 𝐴𝐹𝑥 |
8 | 7, 5 | cio 5766 | . . 3 class (℩𝑥𝐴𝐹𝑥) |
9 | cvv 3173 | . . 3 class V | |
10 | 4, 8, 9 | cif 4036 | . 2 class if(𝐹 defAt 𝐴, (℩𝑥𝐴𝐹𝑥), V) |
11 | 3, 10 | wceq 1475 | 1 wff (𝐹'''𝐴) = if(𝐹 defAt 𝐴, (℩𝑥𝐴𝐹𝑥), V) |
Colors of variables: wff setvar class |
This definition is referenced by: dfafv2 39861 |
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