Theorem 3lt7

Description: 3 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	3lt7	⊢ 3 < 7

Proof

Step	Hyp	Ref	Expression
1		3lt4	⊢ 3 < 4
2		4lt7	⊢ 4 < 7
3		3re	⊢ 3 ∈ ℝ
4		4re	⊢ 4 ∈ ℝ
5		7re	⊢ 7 ∈ ℝ
6	3 4 5	lttri	⊢ ( ( 3 < 4 ∧ 4 < 7 ) → 3 < 7 )
7	1 2 6	mp2an	⊢ 3 < 7