Theorem ovsn

Description: The operation value of a singleton of a nested ordered pair is the last member. (Contributed by Zhi Wang, 22-Oct-2025)

	Ref	Expression
Hypothesis	ovsn.1	⊢ 𝐶 ∈ V
Assertion	ovsn	⊢ ( 𝐴 { ⟨ ⟨ 𝐴 , 𝐵 ⟩ , 𝐶 ⟩ } 𝐵 ) = 𝐶

Proof

Step	Hyp	Ref	Expression
1		ovsn.1	⊢ 𝐶 ∈ V
2		ovsng	⊢ ( 𝐶 ∈ V → ( 𝐴 { ⟨ ⟨ 𝐴 , 𝐵 ⟩ , 𝐶 ⟩ } 𝐵 ) = 𝐶 )
3	1 2	ax-mp	⊢ ( 𝐴 { ⟨ ⟨ 𝐴 , 𝐵 ⟩ , 𝐶 ⟩ } 𝐵 ) = 𝐶