Theorem dmxrncnvepres2

Description: Domain of the range product with restricted converse epsilon relation. (Contributed by Peter Mazsa, 29-Jan-2026)

	Ref	Expression
Assertion	dmxrncnvepres2	|- dom ( R |X. ( `' _E |` A ) ) = ( A i^i ( dom R \ { (/) } ) )

Proof

Step	Hyp	Ref	Expression
1		dmres	|- dom ( R |` A ) = ( A i^i dom R )
2	1	difeq1i	|- ( dom ( R |` A ) \ { (/) } ) = ( ( A i^i dom R ) \ { (/) } )
3		dmxrncnvepres	|- dom ( R |X. ( `' _E |` A ) ) = ( dom ( R |` A ) \ { (/) } )
4		indif2	|- ( A i^i ( dom R \ { (/) } ) ) = ( ( A i^i dom R ) \ { (/) } )
5	2 3 4	3eqtr4i	|- dom ( R |X. ( `' _E |` A ) ) = ( A i^i ( dom R \ { (/) } ) )