Metamath Proof Explorer

Theorem 1nq

Description: The positive fraction 'one'. (Contributed by NM, 29-Oct-1995) (Revised by Mario Carneiro, 28-Apr-2013) (New usage is discouraged.)

Ref Expression
Assertion 1nq 
|- 1Q e. Q.

Proof

Step Hyp Ref Expression
1 df-1nq 
 |-  1Q = <. 1o , 1o >.
2 1pi 
 |-  1o e. N.
3 pinq 
 |-  ( 1o e. N. -> <. 1o , 1o >. e. Q. )
4 2 3 ax-mp 
 |-  <. 1o , 1o >. e. Q.
5 1 4 eqeltri 
 |-  1Q e. Q.