Metamath Proof Explorer

Theorem resdm

Description: A relation restricted to its domain equals itself. (Contributed by NM, 12-Dec-2006)

Ref Expression
Assertion resdm 
|- ( Rel A -> ( A |` dom A ) = A )

Proof

Step Hyp Ref Expression
1 ssid 
 |-  dom A C_ dom A
2 relssres 
 |-  ( ( Rel A /\ dom A C_ dom A ) -> ( A |` dom A ) = A )
3 1 2 mpan2 
 |-  ( Rel A -> ( A |` dom A ) = A )