Metamath Proof Explorer


Theorem 3lt9

Description: 3 is less than 9. (Contributed by Mario Carneiro, 9-Mar-2015)

Ref Expression
Assertion 3lt9 3 < 9

Proof

Step Hyp Ref Expression
1 3lt4 3 < 4
2 4lt9 4 < 9
3 3re 3 ∈ ℝ
4 4re 4 ∈ ℝ
5 9re 9 ∈ ℝ
6 3 4 5 lttri ( ( 3 < 4 ∧ 4 < 9 ) → 3 < 9 )
7 1 2 6 mp2an 3 < 9