Definition df-goan 33302

Description: Define the Godel-set of conjunction. Here the arguments 𝑈 and 𝑉 are also Godel-sets corresponding to smaller formulas. (Contributed by Mario Carneiro, 14-Jul-2013.)

Assertion

Ref	Expression
df-goan	⊢ ∧𝑔 = (𝑢 ∈ V, 𝑣 ∈ V ↦ ¬𝑔(𝑢⊼𝑔𝑣))

Distinct variable group:   𝑣,𝑢

Detailed syntax breakdown of Definition df-goan

Step	Hyp	Ref	Expression
1		cgoa 33295	. 2 class ∧𝑔
2		vu	. . 3 setvar 𝑢
3		vv	. . 3 setvar 𝑣
4		cvv 3422	. . 3 class V
5	2	cv 1538	. . . . 5 class 𝑢
6	3	cv 1538	. . . . 5 class 𝑣
7		cgna 33196	. . . . 5 class ⊼𝑔
8	5, 6, 7	co 7255	. . . 4 class (𝑢⊼𝑔𝑣)
9	8	cgon 33294	. . 3 class ¬𝑔(𝑢⊼𝑔𝑣)
10	2, 3, 4, 4, 9	cmpo 7257	. 2 class (𝑢 ∈ V, 𝑣 ∈ V ↦ ¬𝑔(𝑢⊼𝑔𝑣))
11	1, 10	wceq 1539	1 wff ∧𝑔 = (𝑢 ∈ V, 𝑣 ∈ V ↦ ¬𝑔(𝑢⊼𝑔𝑣))

This definition is referenced by: (None)