Theorem 2lt5

Description: 2 is less than 5. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	2lt5	⊢ 2 < 5

Proof

Step	Hyp	Ref	Expression
1		2lt4	⊢ 2 < 4
2		4lt5	⊢ 4 < 5
3		2re	⊢ 2 ∈ ℝ
4		4re	⊢ 4 ∈ ℝ
5		5re	⊢ 5 ∈ ℝ
6	3 4 5	lttri	⊢ ( ( 2 < 4 ∧ 4 < 5 ) → 2 < 5 )
7	1 2 6	mp2an	⊢ 2 < 5