Metamath Proof Explorer

Theorem 7lt10

Description: 7 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015) (Revised by AV, 8-Sep-2021)

Ref Expression
Assertion 7lt10 
|- 7 < ; 1 0

Proof

Step Hyp Ref Expression
1 7lt8 
 |-  7 < 8
2 8lt10 
 |-  8 < ; 1 0
3 7re 
 |-  7 e. RR
4 8re 
 |-  8 e. RR
5 10re 
 |-  ; 1 0 e. RR
6 3 4 5 lttri 
 |-  ( ( 7 < 8 /\ 8 < ; 1 0 ) -> 7 < ; 1 0 )
7 1 2 6 mp2an 
 |-  7 < ; 1 0