Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
The empty set
ne0i
Next ⟩
ne0d
Metamath Proof Explorer
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Theorem
ne0i
Description:
If a class has elements, then it is nonempty.
(Contributed by
NM
, 31-Dec-1993)
Ref
Expression
Assertion
ne0i
⊢
B
∈
A
→
A
≠
∅
Proof
Step
Hyp
Ref
Expression
1
n0i
⊢
B
∈
A
→
¬
A
=
∅
2
1
neqned
⊢
B
∈
A
→
A
≠
∅