Theorem ressucdifsn2

Description: The difference between restrictions to the successor and the singleton of a class is the restriction to the class, see ressucdifsn . (Contributed by Peter Mazsa, 24-Jul-2024)

	Ref	Expression
Assertion	ressucdifsn2	|- ( ( R |` ( A u. { A } ) ) \ ( R |` { A } ) ) = ( R |` A )

Proof

Step	Hyp	Ref	Expression
1		disjcsn	|- ( A i^i { A } ) = (/)
2		disjresundif	|- ( ( A i^i { A } ) = (/) -> ( ( R |` ( A u. { A } ) ) \ ( R |` { A } ) ) = ( R |` A ) )
3	1 2	ax-mp	|- ( ( R |` ( A u. { A } ) ) \ ( R |` { A } ) ) = ( R |` A )