Theorem 7lt10

Description: 7 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015) (Revised by AV, 8-Sep-2021)

	Ref	Expression
Assertion	7lt10	⊢ 7 < ; 1 0

Proof

Step	Hyp	Ref	Expression
1		7lt8	⊢ 7 < 8
2		8lt10	⊢ 8 < ; 1 0
3		7re	⊢ 7 ∈ ℝ
4		8re	⊢ 8 ∈ ℝ
5		10re	⊢ ; 1 0 ∈ ℝ
6	3 4 5	lttri	⊢ ( ( 7 < 8 ∧ 8 < ; 1 0 ) → 7 < ; 1 0 )
7	1 2 6	mp2an	⊢ 7 < ; 1 0