Database
SUPPLEMENTARY MATERIAL (USERS' MATHBOXES)
Mathbox for BJ
Set theory
Moore collections (complements)
bj-0nmoore
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bj-snmoore
Metamath Proof Explorer
Ascii
Structured
Theorem
bj-0nmoore
Description:
The empty set is not a Moore collection.
(Contributed by
BJ
, 9-Dec-2021)
Ref
Expression
Assertion
bj-0nmoore
⊢
¬ ∅ ∈
Moore
Proof
Step
Hyp
Ref
Expression
1
noel
⊢
¬
∪
∅ ∈ ∅
2
bj-ismoored0
⊢
( ∅ ∈
Moore
→
∪
∅ ∈ ∅ )
3
1
2
mto
⊢
¬ ∅ ∈
Moore