Metamath Proof Explorer

Theorem 6lt10

Description: 6 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015) (Revised by AV, 8-Sep-2021)

Ref Expression
Assertion 6lt10 
|- 6 < ; 1 0

Proof

Step Hyp Ref Expression
1 6lt7 
 |-  6 < 7
2 7lt10 
 |-  7 < ; 1 0
3 6re 
 |-  6 e. RR
4 7re 
 |-  7 e. RR
5 10re 
 |-  ; 1 0 e. RR
6 3 4 5 lttri 
 |-  ( ( 6 < 7 /\ 7 < ; 1 0 ) -> 6 < ; 1 0 )
7 1 2 6 mp2an 
 |-  6 < ; 1 0