Theorem cosni

Description: Composition with an ordered pair singleton. (Contributed by Zhi Wang, 6-Oct-2025)

	Ref	Expression
Hypotheses	cosni.1	|- B e. _V
	cosni.2	|- C e. _V
Assertion	cosni	|- ( A o. { <. B , C >. } ) = ( { B } X. ( A " { C } ) )

Proof

Step	Hyp	Ref	Expression
1		cosni.1	|- B e. _V
2		cosni.2	|- C e. _V
3		cosn	|- ( ( B e. _V /\ C e. _V ) -> ( A o. { <. B , C >. } ) = ( { B } X. ( A " { C } ) ) )
4	1 2 3	mp2an	|- ( A o. { <. B , C >. } ) = ( { B } X. ( A " { C } ) )