Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
The empty set
n0i
Next ⟩
ne0i
Metamath Proof Explorer
Ascii
Unicode
Theorem
n0i
Description:
If a class has elements, then it is not empty.
(Contributed by
NM
, 31-Dec-1993)
Ref
Expression
Assertion
n0i
⊢
B
∈
A
→
¬
A
=
∅
Proof
Step
Hyp
Ref
Expression
1
nel02
⊢
A
=
∅
→
¬
B
∈
A
2
1
con2i
⊢
B
∈
A
→
¬
A
=
∅