Definition df-goal 32875

Description: Define the Godel-set of universal quantification. Here 𝑁 ∈ ω corresponds to v_N , 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

Step	Hyp	Ref	Expression
1		cU	. . 3 class 𝑈
2		cN	. . 3 class 𝑁
3	1, 2	cgol 32868	. 2 class ∀𝑔𝑁𝑈
4		c2o 8125	. . 3 class 2o
5	2, 1	cop 4522	. . 3 class ⟨𝑁, 𝑈⟩
6	4, 5	cop 4522	. 2 class ⟨2o, ⟨𝑁, 𝑈⟩⟩
7	3, 6	wceq 1542	1 wff ∀𝑔𝑁𝑈 = ⟨2o, ⟨𝑁, 𝑈⟩⟩

This definition is referenced by:  goaleq12d  32884  gonanegoal  32885  sat1el2xp  32912  fmlaomn0  32923  goaln0  32926  goalrlem  32929  goalr  32930  fmla0disjsuc  32931  fmlasucdisj  32932  satffunlem1lem1  32935  satffunlem2lem1  32937