Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Unordered and ordered pairs
elsni
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Metamath Proof Explorer
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Theorem
elsni
Description:
There is at most one element in a singleton.
(Contributed by
NM
, 5-Jun-1994)
Ref
Expression
Assertion
elsni
⊢
A
∈
B
→
A
=
B
Proof
Step
Hyp
Ref
Expression
1
elsng
⊢
A
∈
B
→
A
∈
B
↔
A
=
B
2
1
ibi
⊢
A
∈
B
→
A
=
B