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.