Metamath Proof Explorer
Theorem 1pr
Description: The positive real number 'one'. (Contributed by NM, 13-Mar-1996)
(Revised by Mario Carneiro, 12-Jun-2013) (New usage is discouraged.)
|
|
Ref |
Expression |
|
Assertion |
1pr |
|- 1P e. P. |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
df-1p |
|- 1P = { x | x |
2 |
|
1nq |
|- 1Q e. Q. |
3 |
|
nqpr |
|- ( 1Q e. Q. -> { x | x |
4 |
2 3
|
ax-mp |
|- { x | x |
5 |
1 4
|
eqeltri |
|- 1P e. P. |