Definition df-gdlop4

Description: Define the fourth Gödel operation. This function takes two arguments and returns the first argument restricted to the second argument (see df-res ). Based on the fourth case of Definition 14.2 of TakeutiZaring p. 144. (Contributed by BTernaryTau, 2-Sep-2026)

	Ref	Expression
Assertion	df-gdlop4	⊢ ℱ4 = ( 𝑥 ∈ V , 𝑦 ∈ V ↦ ( 𝑥 ↾ 𝑦 ) )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cgdlop4	⊢ ℱ4
1		vx	⊢ 𝑥
2		cvv	⊢ V
3		vy	⊢ 𝑦
4	1	cv	⊢ 𝑥
5	3	cv	⊢ 𝑦
6	4 5	cres	⊢ ( 𝑥 ↾ 𝑦 )
7	1 3 2 2 6	cmpo	⊢ ( 𝑥 ∈ V , 𝑦 ∈ V ↦ ( 𝑥 ↾ 𝑦 ) )
8	0 7	wceq	⊢ ℱ4 = ( 𝑥 ∈ V , 𝑦 ∈ V ↦ ( 𝑥 ↾ 𝑦 ) )