Theorem idinxpresid

Description: The intersection of the identity relation with the cartesian square of a class is the restriction of the identity relation to that class. (Contributed by FL, 2-Aug-2009) (Proof shortened by Peter Mazsa, 9-Sep-2022) (Proof shortened by BJ, 23-Dec-2023)

	Ref	Expression
Assertion	idinxpresid	|- ( _I i^i ( A X. A ) ) = ( _I |` A )

Proof

Step	Hyp	Ref	Expression
1		idinxpres	|- ( _I i^i ( A X. A ) ) = ( _I |` ( A i^i A ) )
2		inidm	|- ( A i^i A ) = A
3	2	reseq2i	|- ( _I |` ( A i^i A ) ) = ( _I |` A )
4	1 3	eqtri	|- ( _I i^i ( A X. A ) ) = ( _I |` A )