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SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
Mathbox for Peter Mazsa
Equivalence relations
eqvrelrel
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eqvrelrefrel
Metamath Proof Explorer
Ascii
Unicode
Theorem
eqvrelrel
Description:
An equivalence relation is a relation.
(Contributed by
Peter Mazsa
, 2-Jun-2019)
Ref
Expression
Assertion
eqvrelrel
⊢
EqvRel
R
→
Rel
⁡
R
Proof
Step
Hyp
Ref
Expression
1
dfeqvrel2
⊢
EqvRel
R
↔
I
↾
dom
⁡
R
⊆
R
∧
R
-1
⊆
R
∧
R
∘
R
⊆
R
∧
Rel
⁡
R
2
1
simprbi
⊢
EqvRel
R
→
Rel
⁡
R