Definition df-goor 33117

Description: Define the Godel-set of disjunction. 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-goor	⊢ ∨𝑔 = (𝑢 ∈ V, 𝑣 ∈ V ↦ (¬𝑔𝑢 →𝑔 𝑣))

Distinct variable group:   𝑣,𝑢

Detailed syntax breakdown of Definition df-goor

Step	Hyp	Ref	Expression
1		cgoo 33110	. 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	5	cgon 33107	. . . 4 class ¬𝑔𝑢
7	3	cv 1542	. . . 4 class 𝑣
8		cgoi 33109	. . . 4 class →𝑔
9	6, 7, 8	co 7213	. . 3 class (¬𝑔𝑢 →𝑔 𝑣)
10	2, 3, 4, 4, 9	cmpo 7215	. 2 class (𝑢 ∈ V, 𝑣 ∈ V ↦ (¬𝑔𝑢 →𝑔 𝑣))
11	1, 10	wceq 1543	1 wff ∨𝑔 = (𝑢 ∈ V, 𝑣 ∈ V ↦ (¬𝑔𝑢 →𝑔 𝑣))

This definition is referenced by: (None)