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Definition df-goim 32867
 Description: Define the Godel-set of implication. 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-goim 𝑔 = (𝑢 ∈ V, 𝑣 ∈ V ↦ (𝑢𝑔¬𝑔𝑣))
Distinct variable group:   𝑣,𝑢

Detailed syntax breakdown of Definition df-goim
StepHypRef Expression
1 cgoi 32860 . 2 class 𝑔
2 vu . . 3 setvar 𝑢
3 vv . . 3 setvar 𝑣
4 cvv 3442 . . 3 class V
52cv 1537 . . . 4 class 𝑢
63cv 1537 . . . . 5 class 𝑣
76cgon 32858 . . . 4 class ¬𝑔𝑣
8 cgna 32760 . . . 4 class 𝑔
95, 7, 8co 7145 . . 3 class (𝑢𝑔¬𝑔𝑣)
102, 3, 4, 4, 9cmpo 7147 . 2 class (𝑢 ∈ V, 𝑣 ∈ V ↦ (𝑢𝑔¬𝑔𝑣))
111, 10wceq 1538 1 wff 𝑔 = (𝑢 ∈ V, 𝑣 ∈ V ↦ (𝑢𝑔¬𝑔𝑣))
 Colors of variables: wff setvar class This definition is referenced by: (None)
 Copyright terms: Public domain W3C validator