This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: A monoid is a semigroup with an identity element. (Contributed by FL, 2-Nov-2009) (New usage is discouraged.)
|
|
Ref |
Expression |
|
Assertion |
df-mndo |
⊢ MndOp = ( SemiGrp ∩ ExId ) |
Detailed syntax breakdown
| Step |
Hyp |
Ref |
Expression |
| 0 |
|
cmndo |
⊢ MndOp |
| 1 |
|
csem |
⊢ SemiGrp |
| 2 |
|
cexid |
⊢ ExId |
| 3 |
1 2
|
cin |
⊢ ( SemiGrp ∩ ExId ) |
| 4 |
0 3
|
wceq |
⊢ MndOp = ( SemiGrp ∩ ExId ) |