Metamath Proof Explorer


Theorem 4lt7

Description: 4 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013)

Ref Expression
Assertion 4lt7 4 < 7

Proof

Step Hyp Ref Expression
1 4lt5 4 < 5
2 5lt7 5 < 7
3 4re 4 ∈ ℝ
4 5re 5 ∈ ℝ
5 7re 7 ∈ ℝ
6 3 4 5 lttri ( ( 4 < 5 ∧ 5 < 7 ) → 4 < 7 )
7 1 2 6 mp2an 4 < 7