Metamath Proof Explorer


Theorem 7lt9

Description: 7 is less than 9. (Contributed by Mario Carneiro, 9-Mar-2015)

Ref Expression
Assertion 7lt9 7 < 9

Proof

Step Hyp Ref Expression
1 7lt8 7 < 8
2 8lt9 8 < 9
3 7re 7 ∈ ℝ
4 8re 8 ∈ ℝ
5 9re 9 ∈ ℝ
6 3 4 5 lttri ( ( 7 < 8 ∧ 8 < 9 ) → 7 < 9 )
7 1 2 6 mp2an 7 < 9