Database
BASIC ALGEBRAIC STRUCTURES
Division rings and fields
Definition and basic properties
df-field
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isdrng
Metamath Proof Explorer
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Definition
df-field
Description:
A
field
is a commutative division ring.
(Contributed by
Mario Carneiro
, 17-Jun-2015)
Ref
Expression
Assertion
df-field
⊢
Field
=
DivRing
∩
CRing
Detailed syntax breakdown
Step
Hyp
Ref
Expression
0
cfield
class
Field
1
cdr
class
DivRing
2
ccrg
class
CRing
3
1
2
cin
class
DivRing
∩
CRing
4
0
3
wceq
wff
Field
=
DivRing
∩
CRing