Definition df-gdlop2 35955

Description: Define the second Gödel operation. This function takes two arguments and returns the intersection of the first argument with the membership relation (see df-in 4094 and df-eprel 5555). The second argument is ignored. Based on the second case of Definition 14.2 of [TakeutiZaring] p. 144. (Contributed by BTernaryTau, 2-Sep-2026.)

Assertion

Ref	Expression
df-gdlop2	⊢ ℱ2 = (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑥 ∩ E ))

Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-gdlop2

Step	Hyp	Ref	Expression
1		cgdlop2 35944	. 2 class ℱ2
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		cvv 3454	. . 3 class V
5	2	cv 1569	. . . 4 class 𝑥
6		cep 5554	. . . 4 class E
7	5, 6	cin 4092	. . 3 class (𝑥 ∩ E )
8	2, 3, 4, 4, 7	cmpo 7445	. 2 class (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑥 ∩ E ))
9	1, 8	wceq 1570	1 wff ℱ2 = (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑥 ∩ E ))

This definition is used by:  gdlop2fv  35964