Definition df-gdlop3 35781

Description: Define the third Gödel operation. This function takes two arguments and returns the first argument minus the second argument (see df-dif 3901). Based on the third case of Definition 14.2 of [TakeutiZaring] p. 144. (Contributed by BTernaryTau, 2-Sep-2026.)

Assertion

Ref	Expression
df-gdlop3	⊢ ℱ3 = (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑥 ∖ 𝑦))

Distinct variable group:   𝑥,𝑦

Detailed syntax breakdown of Definition df-gdlop3

Step	Hyp	Ref	Expression
1		cgdlop3 35770	. 2 class ℱ3
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	cdif 3895	. . 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 ℱ3 = (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑥 ∖ 𝑦))

This definition is used by: (None)