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Mirrors > Home > MPE Home > Th. List > df-undef | Structured version Visualization version GIF version |
Description: Define the undefined value function, whose value at set 𝑠 is guaranteed not to be a member of 𝑠 (see pwuninel 8098). (Contributed by NM, 15-Sep-2011.) |
Ref | Expression |
---|---|
df-undef | ⊢ Undef = (𝑠 ∈ V ↦ 𝒫 ∪ 𝑠) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cund 8095 | . 2 class Undef | |
2 | vs | . . 3 setvar 𝑠 | |
3 | cvv 3431 | . . 3 class V | |
4 | 2 | cv 1537 | . . . . 5 class 𝑠 |
5 | 4 | cuni 4838 | . . . 4 class ∪ 𝑠 |
6 | 5 | cpw 4532 | . . 3 class 𝒫 ∪ 𝑠 |
7 | 2, 3, 6 | cmpt 5156 | . 2 class (𝑠 ∈ V ↦ 𝒫 ∪ 𝑠) |
8 | 1, 7 | wceq 1538 | 1 wff Undef = (𝑠 ∈ V ↦ 𝒫 ∪ 𝑠) |
Colors of variables: wff setvar class |
This definition is referenced by: undefval 8099 |
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