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Definition df-goal 33210
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 33203 . 2 class 𝑔𝑁𝑈
4 c2o 8262 . . 3 class 2o
52, 1cop 4565 . . 3 class 𝑁, 𝑈
64, 5cop 4565 . 2 class ⟨2o, ⟨𝑁, 𝑈⟩⟩
73, 6wceq 1539 1 wff 𝑔𝑁𝑈 = ⟨2o, ⟨𝑁, 𝑈⟩⟩
Colors of variables: wff setvar class
This definition is referenced by:  goaleq12d  33219  gonanegoal  33220  sat1el2xp  33247  fmlaomn0  33258  goaln0  33261  goalrlem  33264  goalr  33265  fmla0disjsuc  33266  fmlasucdisj  33267  satffunlem1lem1  33270  satffunlem2lem1  33272
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