Metamath Proof Explorer

Theorem 3lt10

Description: 3 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015) (Revised by AV, 8-Sep-2021)

Ref Expression
Assertion 3lt10 
|- 3 < ; 1 0

Proof

Step Hyp Ref Expression
1 3lt4 
 |-  3 < 4
2 4lt10 
 |-  4 < ; 1 0
3 3re 
 |-  3 e. RR
4 4re 
 |-  4 e. RR
5 10re 
 |-  ; 1 0 e. RR
6 3 4 5 lttri 
 |-  ( ( 3 < 4 /\ 4 < ; 1 0 ) -> 3 < ; 1 0 )
7 1 2 6 mp2an 
 |-  3 < ; 1 0