Definition df-goim 33116

Description: Define the Godel-set of implication. 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-goim	⊢ →𝑔 = (𝑢 ∈ V, 𝑣 ∈ V ↦ (𝑢⊼𝑔¬𝑔𝑣))

Distinct variable group:   𝑣,𝑢

Detailed syntax breakdown of Definition df-goim

Step	Hyp	Ref	Expression
1		cgoi 33109	. 2 class →𝑔
2		vu	. . 3 setvar 𝑢
3		vv	. . 3 setvar 𝑣
4		cvv 3408	. . 3 class V
5	2	cv 1542	. . . 4 class 𝑢
6	3	cv 1542	. . . . 5 class 𝑣
7	6	cgon 33107	. . . 4 class ¬𝑔𝑣
8		cgna 33009	. . . 4 class ⊼𝑔
9	5, 7, 8	co 7213	. . 3 class (𝑢⊼𝑔¬𝑔𝑣)
10	2, 3, 4, 4, 9	cmpo 7215	. 2 class (𝑢 ∈ V, 𝑣 ∈ V ↦ (𝑢⊼𝑔¬𝑔𝑣))
11	1, 10	wceq 1543	1 wff →𝑔 = (𝑢 ∈ V, 𝑣 ∈ V ↦ (𝑢⊼𝑔¬𝑔𝑣))

This definition is referenced by: (None)