Definition df-gobi 33118

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

Assertion

Ref	Expression
df-gobi	⊢ ↔𝑔 = (𝑢 ∈ V, 𝑣 ∈ 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 33111	. 2 class ↔𝑔
2		vu	. . 3 setvar 𝑢
3		vv	. . 3 setvar 𝑣
4		cvv 3408	. . 3 class V
5	2	cv 1542	. . . . 5 class 𝑢
6	3	cv 1542	. . . . 5 class 𝑣
7		cgoi 33109	. . . . 5 class →𝑔
8	5, 6, 7	co 7213	. . . 4 class (𝑢 →𝑔 𝑣)
9	6, 5, 7	co 7213	. . . 4 class (𝑣 →𝑔 𝑢)
10		cgoa 33108	. . . 4 class ∧𝑔
11	8, 9, 10	co 7213	. . 3 class ((𝑢 →𝑔 𝑣)∧𝑔(𝑣 →𝑔 𝑢))
12	2, 3, 4, 4, 11	cmpo 7215	. 2 class (𝑢 ∈ V, 𝑣 ∈ V ↦ ((𝑢 →𝑔 𝑣)∧𝑔(𝑣 →𝑔 𝑢)))
13	1, 12	wceq 1543	1 wff ↔𝑔 = (𝑢 ∈ V, 𝑣 ∈ V ↦ ((𝑢 →𝑔 𝑣)∧𝑔(𝑣 →𝑔 𝑢)))

This definition is referenced by: (None)