Definition df-gdlop5 35783

Description: Define the fifth Gödel operation. This function takes two arguments and returns the intersection of the first argument with the domain of the second argument (see df-in 3905 and df-dm 5657). Based on the fifth case of Definition 14.2 of [TakeutiZaring] p. 144. (Contributed by BTernaryTau, 2-Sep-2026.)

Assertion

Ref	Expression
df-gdlop5	⊢ ℱ5 = (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑥 ∩ dom 𝑦))

Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-gdlop5

Step	Hyp	Ref	Expression
1		cgdlop5 35772	. 2 class ℱ5
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		cvv 3450	. . 3 class V
5	2	cv 1569	. . . 4 class 𝑥
6	3	cv 1569	. . . . 5 class 𝑦
7	6	cdm 5647	. . . 4 class dom 𝑦
8	5, 7	cin 3897	. . 3 class (𝑥 ∩ dom 𝑦)
9	2, 3, 4, 4, 8	cmpo 7410	. 2 class (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑥 ∩ dom 𝑦))
10	1, 9	wceq 1570	1 wff ℱ5 = (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑥 ∩ dom 𝑦))

This definition is used by: (None)