Theorem intimasn2

Description: Two ways to express the image of a singleton when the relation is an intersection. (Contributed by RP, 13-Apr-2020)

	Ref	Expression
Assertion	intimasn2	|- ( B e. V -> ( |^| A " { B } ) = |^|_ x e. A ( x " { B } ) )

Proof

Step	Hyp	Ref	Expression
1		intimasn	|- ( B e. V -> ( |^| A " { B } ) = |^| { y | E. x e. A y = ( x " { B } ) } )
2		intima0	|- |^|_ x e. A ( x " { B } ) = |^| { y | E. x e. A y = ( x " { B } ) }
3	1 2	eqtr4di	|- ( B e. V -> ( |^| A " { B } ) = |^|_ x e. A ( x " { B } ) )