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Metamath Proof Explorer

Theorem 2lt10

Description: 2 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015) (Revised by AV, 8-Sep-2021)

Ref Expression
Assertion 2lt10 
|- 2 < ; 1 0

Proof

Step Hyp Ref Expression
1 2lt3 
 |-  2 < 3
2 3lt10 
 |-  3 < ; 1 0
3 2re 
 |-  2 e. RR
4 3re 
 |-  3 e. RR
5 10re 
 |-  ; 1 0 e. RR
6 3 4 5 lttri 
 |-  ( ( 2 < 3 /\ 3 < ; 1 0 ) -> 2 < ; 1 0 )
7 1 2 6 mp2an 
 |-  2 < ; 1 0