Definition df-gdlop5

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 and df-dm ). Based on the fifth case of Definition 14.2 of TakeutiZaring p. 144. (Contributed by BTernaryTau, 2-Sep-2026)

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

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cgdlop5	⊢ ℱ5
1		vx	⊢ 𝑥
2		cvv	⊢ V
3		vy	⊢ 𝑦
4	1	cv	⊢ 𝑥
5	3	cv	⊢ 𝑦
6	5	cdm	⊢ dom 𝑦
7	4 6	cin	⊢ ( 𝑥 ∩ dom 𝑦 )
8	1 3 2 2 7	cmpo	⊢ ( 𝑥 ∈ V , 𝑦 ∈ V ↦ ( 𝑥 ∩ dom 𝑦 ) )
9	0 8	wceq	⊢ ℱ5 = ( 𝑥 ∈ V , 𝑦 ∈ V ↦ ( 𝑥 ∩ dom 𝑦 ) )