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

Proof

Step	Hyp	Ref	Expression
1		ovsn.1	$$⊢C\in \mathrm{V}$$
2		ovsng	$$⊢C\in \mathrm{V}\to A\left\{⟨⟨A,B⟩,C⟩\right\}B=C$$
3	1 2	ax-mp	$$⊢A\left\{⟨⟨A,B⟩,C⟩\right\}B=C$$