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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 )