Metamath Proof Explorer


Theorem 2lt6

Description: 2 is less than 6. (Contributed by Mario Carneiro, 15-Sep-2013)

Ref Expression
Assertion 2lt6
|- 2 < 6

Proof

Step Hyp Ref Expression
1 2lt3
 |-  2 < 3
2 3lt6
 |-  3 < 6
3 2re
 |-  2 e. RR
4 3re
 |-  3 e. RR
5 6re
 |-  6 e. RR
6 3 4 5 lttri
 |-  ( ( 2 < 3 /\ 3 < 6 ) -> 2 < 6 )
7 1 2 6 mp2an
 |-  2 < 6