Metamath Proof Explorer


Theorem eqvrelim

Description: Equivalence relation implies that the domain and the range are equal. (Contributed by Peter Mazsa, 29-Dec-2021)

Ref Expression
Assertion eqvrelim
|- ( EqvRel R -> dom R = ran R )

Proof

Step Hyp Ref Expression
1 eqvrelsymrel
 |-  ( EqvRel R -> SymRel R )
2 symrelim
 |-  ( SymRel R -> dom R = ran R )
3 1 2 syl
 |-  ( EqvRel R -> dom R = ran R )