Theorem pr01ssre

Description: The range of the indicator function is a subset of RR . (Contributed by Thierry Arnoux, 14-Aug-2017)

	Ref	Expression
Assertion	pr01ssre	⊢ { 0 , 1 } ⊆ ℝ

Proof

Step	Hyp	Ref	Expression
1		0re	⊢ 0 ∈ ℝ
2		1re	⊢ 1 ∈ ℝ
3		prssi	⊢ ( ( 0 ∈ ℝ ∧ 1 ∈ ℝ ) → { 0 , 1 } ⊆ ℝ )
4	1 2 3	mp2an	⊢ { 0 , 1 } ⊆ ℝ