Definition df-goal

Description: Define the Godel-set of universal quantification. Here N e.om corresponds to vN , and U represents another formula, and this expression is [ A. x ph ] = A.g N U where x is the N -th variable, U = [ ph ] is the code for ph . Note that this is a class expression, not a wff. (Contributed by Mario Carneiro, 14-Jul-2013)

	Ref	Expression
Assertion	df-goal	$$⊢\left[{\forall }_{𝑔}NU\right]=⟨2_{𝑜},⟨N,U⟩⟩$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cN	$$classN$$
1		cU	$$classU$$
2	1 0	cgol	$$class\left[{\forall }_{𝑔}NU\right]$$
3		c2o	$$class{2}_{𝑜}$$
4	0 1	cop	$$class⟨N,U⟩$$
5	3 4	cop	$$class⟨2_{𝑜},⟨N,U⟩⟩$$
6	2 5	wceq	$$wff\left[{\forall }_{𝑔}NU\right]=⟨2_{𝑜},⟨N,U⟩⟩$$