Database
REAL AND COMPLEX NUMBERS
Reflexive and transitive closures of relations
The reflexive and transitive properties of relations
0trrel
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Basic properties of closures
Metamath Proof Explorer
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Theorem
0trrel
Description:
The empty class is a transitive relation.
(Contributed by
RP
, 24-Dec-2019)
Ref
Expression
Assertion
0trrel
⊢
∅
∘
∅
⊆
∅
Proof
Step
Hyp
Ref
Expression
1
co01
⊢
∅
∘
∅
=
∅
2
1
eqimssi
⊢
∅
∘
∅
⊆
∅