Theorem ovsng

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
Assertion	ovsng	|- ( C e. V -> ( A { <. <. A , B >. , C >. } B ) = C )

Proof

Step	Hyp	Ref	Expression
1		df-ov	|- ( A { <. <. A , B >. , C >. } B ) = ( { <. <. A , B >. , C >. } ` <. A , B >. )
2		opex	|- <. A , B >. e. _V
3		fvsng	|- ( ( <. A , B >. e. _V /\ C e. V ) -> ( { <. <. A , B >. , C >. } ` <. A , B >. ) = C )
4	2 3	mpan	|- ( C e. V -> ( { <. <. A , B >. , C >. } ` <. A , B >. ) = C )
5	1 4	eqtrid	|- ( C e. V -> ( A { <. <. A , B >. , C >. } B ) = C )