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	$$⊢C\in V\to A\left\{⟨A,B,C⟩\right\}B=C$$

Proof

Step	Hyp	Ref	Expression
1		df-ot	$$⊢⟨A,B,C⟩=⟨⟨A,B⟩,C⟩$$
2	1	sneqi	$$⊢\left\{⟨A,B,C⟩\right\}=\left\{⟨⟨A,B⟩,C⟩\right\}$$
3	2	oveqi	$$⊢A\left\{⟨A,B,C⟩\right\}B=A\left\{⟨⟨A,B⟩,C⟩\right\}B$$
4		ovsng	$$⊢C\in V\to A\left\{⟨⟨A,B⟩,C⟩\right\}B=C$$
5	3 4	eqtrid	$$⊢C\in V\to A\left\{⟨A,B,C⟩\right\}B=C$$