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Definition df-goal 32593
Description: Define the Godel-set of universal quantification. Here 𝑁 ∈ ω corresponds to vN , and 𝑈 represents another formula, and this expression is [∀𝑥𝜑] = ∀𝑔𝑁𝑈 where 𝑥 is the 𝑁-th variable, 𝑈 = [𝜑] is the code for 𝜑. Note that this is a class expression, not a wff. (Contributed by Mario Carneiro, 14-Jul-2013.)
Assertion
Ref Expression
df-goal 𝑔𝑁𝑈 = ⟨2o, ⟨𝑁, 𝑈⟩⟩

Detailed syntax breakdown of Definition df-goal
StepHypRef Expression
1 cU . . 3 class 𝑈
2 cN . . 3 class 𝑁
31, 2cgol 32586 . 2 class 𝑔𝑁𝑈
4 c2o 8099 . . 3 class 2o
52, 1cop 4576 . . 3 class 𝑁, 𝑈
64, 5cop 4576 . 2 class ⟨2o, ⟨𝑁, 𝑈⟩⟩
73, 6wceq 1536 1 wff 𝑔𝑁𝑈 = ⟨2o, ⟨𝑁, 𝑈⟩⟩
Colors of variables: wff setvar class
This definition is referenced by:  goaleq12d  32602  gonanegoal  32603  sat1el2xp  32630  fmlaomn0  32641  goaln0  32644  goalrlem  32647  goalr  32648  fmla0disjsuc  32649  fmlasucdisj  32650  satffunlem1lem1  32653  satffunlem2lem1  32655
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