Database
ZF (ZERMELO-FRAENKEL) SET THEORY
ZF Set Theory - start with the Axiom of Extensionality
The difference, union, and intersection of two classes
The difference of two classes
elndif
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neldif
Metamath Proof Explorer
Ascii
Unicode
Theorem
elndif
Description:
A set does not belong to a class excluding it.
(Contributed by
NM
, 27-Jun-1994)
Ref
Expression
Assertion
elndif
⊢
A
∈
B
→
¬
A
∈
C
∖
B
Proof
Step
Hyp
Ref
Expression
1
eldifn
⊢
A
∈
C
∖
B
→
¬
A
∈
B
2
1
con2i
⊢
A
∈
B
→
¬
A
∈
C
∖
B