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Definition df-gobi 32818
 Description: Define the Godel-set of equivalence. 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-gobi 𝑔 = (𝑢 ∈ V, 𝑣 ∈ V ↦ ((𝑢𝑔 𝑣)∧𝑔(𝑣𝑔 𝑢)))
Distinct variable group:   𝑣,𝑢

Detailed syntax breakdown of Definition df-gobi
StepHypRef Expression
1 cgob 32811 . 2 class 𝑔
2 vu . . 3 setvar 𝑢
3 vv . . 3 setvar 𝑣
4 cvv 3441 . . 3 class V
52cv 1537 . . . . 5 class 𝑢
63cv 1537 . . . . 5 class 𝑣
7 cgoi 32809 . . . . 5 class 𝑔
85, 6, 7co 7136 . . . 4 class (𝑢𝑔 𝑣)
96, 5, 7co 7136 . . . 4 class (𝑣𝑔 𝑢)
10 cgoa 32808 . . . 4 class 𝑔
118, 9, 10co 7136 . . 3 class ((𝑢𝑔 𝑣)∧𝑔(𝑣𝑔 𝑢))
122, 3, 4, 4, 11cmpo 7138 . 2 class (𝑢 ∈ V, 𝑣 ∈ V ↦ ((𝑢𝑔 𝑣)∧𝑔(𝑣𝑔 𝑢)))
131, 12wceq 1538 1 wff 𝑔 = (𝑢 ∈ V, 𝑣 ∈ V ↦ ((𝑢𝑔 𝑣)∧𝑔(𝑣𝑔 𝑢)))
 Colors of variables: wff setvar class This definition is referenced by: (None)
 Copyright terms: Public domain W3C validator