Definition df-gdlop1 35779

Description: Define the first Gödel operation. This function takes two arguments and returns the unordered pair containing both (see df-pr 4586). Based on the first case of Definition 14.2 of [TakeutiZaring] p. 144. (Contributed by BTernaryTau, 2-Sep-2026.)

Assertion

Ref	Expression
df-gdlop1	⊢ ℱ1 = (𝑥 ∈ V, 𝑦 ∈ V ↦ {𝑥, 𝑦})

Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-gdlop1

Step	Hyp	Ref	Expression
1		cgdlop1 35768	. 2 class ℱ1
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	. . . 4 class 𝑦
7	5, 6	cpr 4585	. . 3 class {𝑥, 𝑦}
8	2, 3, 4, 4, 7	cmpo 7410	. 2 class (𝑥 ∈ V, 𝑦 ∈ V ↦ {𝑥, 𝑦})
9	1, 8	wceq 1570	1 wff ℱ1 = (𝑥 ∈ V, 𝑦 ∈ V ↦ {𝑥, 𝑦})

This definition is used by: (None)