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