Definition df-gobi 31339

Description: Define the Godel-set of equivalence. Here the arguments U and V are also Godel-sets corresponding to smaller formulae. Note that this is a class expression, not a wff. (Contributed by Mario Carneiro, 14-Jul-2013.)

Assertion

Ref	Expression
df-gobi	|- <->g = ( u e. _V , v e. _V |-> ( ( u ->g v ) /\g ( v ->g u ) ) )

Distinct variable group:   v, u

Detailed syntax breakdown of Definition df-gobi

Step	Hyp	Ref	Expression
1		cgob 31332	. 2 class <->g
2		vu	. . 3 setvar u
3		vv	. . 3 setvar v
4		cvv 3200	. . 3 class _V
5	2	cv 1482	. . . . 5 class u
6	3	cv 1482	. . . . 5 class v
7		cgoi 31330	. . . . 5 class ->g
8	5, 6, 7	co 6650	. . . 4 class ( u ->g v )
9	6, 5, 7	co 6650	. . . 4 class ( v ->g u )
10		cgoa 31329	. . . 4 class /\g
11	8, 9, 10	co 6650	. . 3 class ( ( u ->g v ) /\g ( v ->g u ) )
12	2, 3, 4, 4, 11	cmpt2 6652	. 2 class ( u e. _V , v e. _V |-> ( ( u ->g v ) /\g ( v ->g u ) ) )
13	1, 12	wceq 1483	1 wff <->g = ( u e. _V , v e. _V |-> ( ( u ->g v ) /\g ( v ->g u ) ) )

This definition is referenced by: (None)