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Metamath Proof Explorer
Definition df-r
Description: Define the set of real numbers. (Contributed by NM, 22-Feb-1996)
(New usage is discouraged.)
|
|
Ref |
Expression |
|
Assertion |
df-r |
⊢ ℝ = ( R × { 0R } ) |
Detailed syntax breakdown
| Step |
Hyp |
Ref |
Expression |
| 0 |
|
cr |
⊢ ℝ |
| 1 |
|
cnr |
⊢ R |
| 2 |
|
c0r |
⊢ 0R |
| 3 |
2
|
csn |
⊢ { 0R } |
| 4 |
1 3
|
cxp |
⊢ ( R × { 0R } ) |
| 5 |
0 4
|
wceq |
⊢ ℝ = ( R × { 0R } ) |