Metamath Proof Explorer
Description: A field is a division ring. (Contributed by Jeff Madsen, 10-Jun-2010)
(Revised by Mario Carneiro, 15-Dec-2013) (New usage is discouraged.)
|
|
Ref |
Expression |
|
Assertion |
flddivrng |
⊢ ( 𝐾 ∈ Fld → 𝐾 ∈ DivRingOps ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
df-fld |
⊢ Fld = ( DivRingOps ∩ Com2 ) |
2 |
|
inss1 |
⊢ ( DivRingOps ∩ Com2 ) ⊆ DivRingOps |
3 |
1 2
|
eqsstri |
⊢ Fld ⊆ DivRingOps |
4 |
3
|
sseli |
⊢ ( 𝐾 ∈ Fld → 𝐾 ∈ DivRingOps ) |