Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Negated equality and membership
Negated membership
nelir
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neleq12d
Metamath Proof Explorer
Ascii
Unicode
Theorem
nelir
Description:
Inference associated with
df-nel
.
(Contributed by
BJ
, 7-Jul-2018)
Ref
Expression
Hypothesis
nelir.1
⊢
¬
A
∈
B
Assertion
nelir
⊢
A
∉
B
Proof
Step
Hyp
Ref
Expression
1
nelir.1
⊢
¬
A
∈
B
2
df-nel
⊢
A
∉
B
↔
¬
A
∈
B
3
1
2
mpbir
⊢
A
∉
B