Metamath Proof Explorer

Theorem 1lt10

Description: 1 is less than 10. (Contributed by NM, 7-Nov-2012) (Revised by Mario Carneiro, 9-Mar-2015) (Revised by AV, 8-Sep-2021)

Ref Expression
Assertion 1lt10 
|- 1 < ; 1 0

Proof

Step Hyp Ref Expression
1 1lt2 
 |-  1 < 2
2 2lt10 
 |-  2 < ; 1 0
3 1re 
 |-  1 e. RR
4 2re 
 |-  2 e. RR
5 10re 
 |-  ; 1 0 e. RR
6 3 4 5 lttri 
 |-  ( ( 1 < 2 /\ 2 < ; 1 0 ) -> 1 < ; 1 0 )
7 1 2 6 mp2an 
 |-  1 < ; 1 0