Metamath Proof Explorer


Theorem 3lt8

Description: 3 is less than 8. (Contributed by Mario Carneiro, 15-Sep-2013)

Ref Expression
Assertion 3lt8
|- 3 < 8

Proof

Step Hyp Ref Expression
1 3lt4
 |-  3 < 4
2 4lt8
 |-  4 < 8
3 3re
 |-  3 e. RR
4 4re
 |-  4 e. RR
5 8re
 |-  8 e. RR
6 3 4 5 lttri
 |-  ( ( 3 < 4 /\ 4 < 8 ) -> 3 < 8 )
7 1 2 6 mp2an
 |-  3 < 8