Theorem 3lt10

Description: 3 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015) (Revised by AV, 8-Sep-2021)

	Ref	Expression
Assertion	3lt10	⊢ 3 < ; 1 0

Proof

Step	Hyp	Ref	Expression
1		3lt4	⊢ 3 < 4
2		4lt10	⊢ 4 < ; 1 0
3		3re	⊢ 3 ∈ ℝ
4		4re	⊢ 4 ∈ ℝ
5		10re	⊢ ; 1 0 ∈ ℝ
6	3 4 5	lttri	⊢ ( ( 3 < 4 ∧ 4 < ; 1 0 ) → 3 < ; 1 0 )
7	1 2 6	mp2an	⊢ 3 < ; 1 0