Definition df-gdlop8 35910

Description: Define the eighth Gödel operation. This function takes two arguments and returns the intersection of the first argument with the third converse of the second argument (see df-in 4091 and df-cnv3 35902). Based on the eighth case of Definition 14.2 of [TakeutiZaring] p. 144. (Contributed by BTernaryTau, 2-Sep-2026.)

Assertion

Ref	Expression
df-gdlop8	⊢ ℱ8 = (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑥 ∩ (Cnv3‘𝑦)))

Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-gdlop8

Step	Hyp	Ref	Expression
1		cgdlop8 35899	. 2 class ℱ8
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		cvv 3450	. . 3 class V
5	2	cv 1568	. . . 4 class 𝑥
6	3	cv 1568	. . . . 5 class 𝑦
7		ccnv3 35891	. . . . 5 class Cnv3
8	6, 7	cfv 6538	. . . 4 class (Cnv3‘𝑦)
9	5, 8	cin 4089	. . 3 class (𝑥 ∩ (Cnv3‘𝑦))
10	2, 3, 4, 4, 9	cmpo 7422	. 2 class (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑥 ∩ (Cnv3‘𝑦)))
11	1, 10	wceq 1569	1 wff ℱ8 = (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑥 ∩ (Cnv3‘𝑦)))

This definition is used by: (None)