Theorem ovsng2

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

	Ref	Expression
Assertion	ovsng2	⊢ ( 𝐶 ∈ 𝑉 → ( 𝐴 { ⟨ 𝐴 , 𝐵 , 𝐶 ⟩ } 𝐵 ) = 𝐶 )

Proof

Step	Hyp	Ref	Expression
1		df-ot	⊢ ⟨ 𝐴 , 𝐵 , 𝐶 ⟩ = ⟨ ⟨ 𝐴 , 𝐵 ⟩ , 𝐶 ⟩
2	1	sneqi	⊢ { ⟨ 𝐴 , 𝐵 , 𝐶 ⟩ } = { ⟨ ⟨ 𝐴 , 𝐵 ⟩ , 𝐶 ⟩ }
3	2	oveqi	⊢ ( 𝐴 { ⟨ 𝐴 , 𝐵 , 𝐶 ⟩ } 𝐵 ) = ( 𝐴 { ⟨ ⟨ 𝐴 , 𝐵 ⟩ , 𝐶 ⟩ } 𝐵 )
4		ovsng	⊢ ( 𝐶 ∈ 𝑉 → ( 𝐴 { ⟨ ⟨ 𝐴 , 𝐵 ⟩ , 𝐶 ⟩ } 𝐵 ) = 𝐶 )
5	3 4	eqtrid	⊢ ( 𝐶 ∈ 𝑉 → ( 𝐴 { ⟨ 𝐴 , 𝐵 , 𝐶 ⟩ } 𝐵 ) = 𝐶 )