Metamath Proof Explorer

Theorem 1lt9

Description: 1 is less than 9. (Contributed by NM, 19-Oct-2012) (Revised by Mario Carneiro, 9-Mar-2015)

Ref Expression
Assertion 1lt9 
|- 1 < 9

Proof

Step Hyp Ref Expression
1 1lt2 
 |-  1 < 2
2 2lt9 
 |-  2 < 9
3 1re 
 |-  1 e. RR
4 2re 
 |-  2 e. RR
5 9re 
 |-  9 e. RR
6 3 4 5 lttri 
 |-  ( ( 1 < 2 /\ 2 < 9 ) -> 1 < 9 )
7 1 2 6 mp2an 
 |-  1 < 9