Metamath Proof Explorer


Theorem resdmdfsn

Description: Restricting a relation to its domain without a set is the same as restricting the relation to the universe without this set. (Contributed by AV, 2-Dec-2018)

Ref Expression
Assertion resdmdfsn RelRRVX=RdomRX

Proof

Step Hyp Ref Expression
1 resindm RelRRVXdomR=RVX
2 indif1 VXdomR=VdomRX
3 incom VdomR=domRV
4 inv1 domRV=domR
5 3 4 eqtri VdomR=domR
6 5 difeq1i VdomRX=domRX
7 2 6 eqtri VXdomR=domRX
8 7 reseq2i RVXdomR=RdomRX
9 1 8 eqtr3di RelRRVX=RdomRX