Metamath Proof Explorer

Theorem 5lt10

Description: 5 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015) (Revised by AV, 8-Sep-2021)

Ref Expression
Assertion 5lt10 
|- 5 < ; 1 0

Proof

Step Hyp Ref Expression
1 5lt6 
 |-  5 < 6
2 6lt10 
 |-  6 < ; 1 0
3 5re 
 |-  5 e. RR
4 6re 
 |-  6 e. RR
5 10re 
 |-  ; 1 0 e. RR
6 3 4 5 lttri 
 |-  ( ( 5 < 6 /\ 6 < ; 1 0 ) -> 5 < ; 1 0 )
7 1 2 6 mp2an 
 |-  5 < ; 1 0