Theorem unitssre

Description: ( 0 , 1 ) is a subset of the reals. (Contributed by David Moews, 28-Feb-2017)

	Ref	Expression
Assertion	unitssre	⊢ ( 0 [,] 1 ) ⊆ ℝ

Proof

Step	Hyp	Ref	Expression
1		0re	⊢ 0 ∈ ℝ
2		1re	⊢ 1 ∈ ℝ
3		iccssre	⊢ ( ( 0 ∈ ℝ ∧ 1 ∈ ℝ ) → ( 0 [,] 1 ) ⊆ ℝ )
4	1 2 3	mp2an	⊢ ( 0 [,] 1 ) ⊆ ℝ