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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-gobi | Structured version Visualization version GIF version |
Description: Define the Godel-set of equivalence. Here the arguments 𝑈 and 𝑉 are also Godel-sets corresponding to smaller formulae. Note that this is a class expression, not a wff. (Contributed by Mario Carneiro, 14-Jul-2013.) |
Ref | Expression |
---|---|
df-gobi | ⊢ ↔𝑔 = (𝑢 ∈ V, 𝑣 ∈ V ↦ ((𝑢 →𝑔 𝑣)∧𝑔(𝑣 →𝑔 𝑢))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cgob 31332 | . 2 class ↔𝑔 | |
2 | vu | . . 3 setvar 𝑢 | |
3 | vv | . . 3 setvar 𝑣 | |
4 | cvv 3200 | . . 3 class V | |
5 | 2 | cv 1482 | . . . . 5 class 𝑢 |
6 | 3 | cv 1482 | . . . . 5 class 𝑣 |
7 | cgoi 31330 | . . . . 5 class →𝑔 | |
8 | 5, 6, 7 | co 6650 | . . . 4 class (𝑢 →𝑔 𝑣) |
9 | 6, 5, 7 | co 6650 | . . . 4 class (𝑣 →𝑔 𝑢) |
10 | cgoa 31329 | . . . 4 class ∧𝑔 | |
11 | 8, 9, 10 | co 6650 | . . 3 class ((𝑢 →𝑔 𝑣)∧𝑔(𝑣 →𝑔 𝑢)) |
12 | 2, 3, 4, 4, 11 | cmpt2 6652 | . 2 class (𝑢 ∈ V, 𝑣 ∈ V ↦ ((𝑢 →𝑔 𝑣)∧𝑔(𝑣 →𝑔 𝑢))) |
13 | 1, 12 | wceq 1483 | 1 wff ↔𝑔 = (𝑢 ∈ V, 𝑣 ∈ V ↦ ((𝑢 →𝑔 𝑣)∧𝑔(𝑣 →𝑔 𝑢))) |
Colors of variables: wff setvar class |
This definition is referenced by: (None) |
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