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Metamath Proof Explorer

Definition df-goex

Description: Define the Godel-set of existential quantification. Here N e.om corresponds to vN , and U represents another formula, and this expression is [ E. x ph ] = E.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-goex	$⊢ [\exists_{𝑔} N U] = [\neg_{𝑔} [\forall_{𝑔} N [\neg_{𝑔} U]]]$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cN	$class N$
1		cU	$class U$
2	1 0	cgox	$class [\exists_{𝑔} N U]$
3	1	cgon	$class [\neg_{𝑔} U]$
4	3 0	cgol	$class [\forall_{𝑔} N [\neg_{𝑔} U]]$
5	4	cgon	$class [\neg_{𝑔} [\forall_{𝑔} N [\neg_{𝑔} U]]]$
6	2 5	wceq	$wff [\exists_{𝑔} N U] = [\neg_{𝑔} [\forall_{𝑔} N [\neg_{𝑔} U]]]$