Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - add the Axiom of Power Sets
Relations
0nelrel
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fconstmpt
Metamath Proof Explorer
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Unicode
Theorem
0nelrel
Description:
A binary relation does not contain the empty set.
(Contributed by
AV
, 15-Nov-2021)
Ref
Expression
Assertion
0nelrel
⊢
Rel
⁡
R
→
∅
∉
R
Proof
Step
Hyp
Ref
Expression
1
0nelrel0
⊢
Rel
⁡
R
→
¬
∅
∈
R
2
df-nel
⊢
∅
∉
R
↔
¬
∅
∈
R
3
1
2
sylibr
⊢
Rel
⁡
R
→
∅
∉
R