Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Negated equality and membership
Negated equality
df-ne
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neii
Metamath Proof Explorer
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Definition
df-ne
Description:
Define inequality.
(Contributed by
NM
, 26-May-1993)
Ref
Expression
Assertion
df-ne
⊢
A
≠
B
↔
¬
A
=
B
Detailed syntax breakdown
Step
Hyp
Ref
Expression
0
cA
class
A
1
cB
class
B
2
0
1
wne
wff
A
≠
B
3
0
1
wceq
wff
A
=
B
4
3
wn
wff
¬
A
=
B
5
2
4
wb
wff
A
≠
B
↔
¬
A
=
B