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Definition df-goor 33117
Description: Define the Godel-set of disjunction. Here the arguments 𝑈 and 𝑉 are also Godel-sets corresponding to smaller formulas. Note that this is a class expression, not a wff. (Contributed by Mario Carneiro, 14-Jul-2013.)
Assertion
Ref Expression
df-goor 𝑔 = (𝑢 ∈ V, 𝑣 ∈ V ↦ (¬𝑔𝑢𝑔 𝑣))
Distinct variable group:   𝑣,𝑢

Detailed syntax breakdown of Definition df-goor
StepHypRef Expression
1 cgoo 33110 . 2 class 𝑔
2 vu . . 3 setvar 𝑢
3 vv . . 3 setvar 𝑣
4 cvv 3408 . . 3 class V
52cv 1542 . . . . 5 class 𝑢
65cgon 33107 . . . 4 class ¬𝑔𝑢
73cv 1542 . . . 4 class 𝑣
8 cgoi 33109 . . . 4 class 𝑔
96, 7, 8co 7213 . . 3 class 𝑔𝑢𝑔 𝑣)
102, 3, 4, 4, 9cmpo 7215 . 2 class (𝑢 ∈ V, 𝑣 ∈ V ↦ (¬𝑔𝑢𝑔 𝑣))
111, 10wceq 1543 1 wff 𝑔 = (𝑢 ∈ V, 𝑣 ∈ V ↦ (¬𝑔𝑢𝑔 𝑣))
Colors of variables: wff setvar class
This definition is referenced by: (None)
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