Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Negated equality and membership
Negated equality
neii
Next ⟩
neir
Metamath Proof Explorer
Ascii
Structured
Theorem
neii
Description:
Inference associated with
df-ne
.
(Contributed by
BJ
, 7-Jul-2018)
Ref
Expression
Hypothesis
neii.1
⊢
𝐴
≠
𝐵
Assertion
neii
⊢
¬
𝐴
=
𝐵
Proof
Step
Hyp
Ref
Expression
1
neii.1
⊢
𝐴
≠
𝐵
2
df-ne
⊢
(
𝐴
≠
𝐵
↔ ¬
𝐴
=
𝐵
)
3
1
2
mpbi
⊢
¬
𝐴
=
𝐵