Users' Mathboxes Mathbox for Mario Carneiro < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  df-goal Structured version   Visualization version   GIF version

Definition df-goal 34328
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 34321 . 2 class 𝑔𝑁𝑈
4 c2o 8459 . . 3 class 2o
52, 1cop 4634 . . 3 class 𝑁, 𝑈
64, 5cop 4634 . 2 class ⟨2o, ⟨𝑁, 𝑈⟩⟩
73, 6wceq 1541 1 wff 𝑔𝑁𝑈 = ⟨2o, ⟨𝑁, 𝑈⟩⟩
Colors of variables: wff setvar class
This definition is referenced by:  goaleq12d  34337  gonanegoal  34338  sat1el2xp  34365  fmlaomn0  34376  goaln0  34379  goalrlem  34382  goalr  34383  fmla0disjsuc  34384  fmlasucdisj  34385  satffunlem1lem1  34388  satffunlem2lem1  34390
  Copyright terms: Public domain W3C validator