Metamath Proof Explorer

Theorem 8lt10

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

Ref Expression
Assertion 8lt10 
|- 8 < ; 1 0

Proof

Step Hyp Ref Expression
1 8lt9 
 |-  8 < 9
2 9lt10 
 |-  9 < ; 1 0
3 8re 
 |-  8 e. RR
4 9re 
 |-  9 e. RR
5 10re 
 |-  ; 1 0 e. RR
6 3 4 5 lttri 
 |-  ( ( 8 < 9 /\ 9 < ; 1 0 ) -> 8 < ; 1 0 )
7 1 2 6 mp2an 
 |-  8 < ; 1 0