Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
Negated equality and membership
Negated equality
neneq
Next ⟩
neqned
Metamath Proof Explorer
Ascii
Unicode
Theorem
neneq
Description:
From inequality to non-equality.
(Contributed by
Glauco Siliprandi
, 11-Dec-2019)
Ref
Expression
Assertion
neneq
⊢
A
≠
B
→
¬
A
=
B
Proof
Step
Hyp
Ref
Expression
1
id
⊢
A
≠
B
→
A
≠
B
2
1
neneqd
⊢
A
≠
B
→
¬
A
=
B