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	$$⊢\left\{0,1\right\}\subseteq ℝ$$

Proof

Step	Hyp	Ref	Expression
1		0re	$$⊢0\in ℝ$$
2		1re	$$⊢1\in ℝ$$
3		prssi	$$⊢\left(0\in ℝ\wedge 1\in ℝ\right)\to \left\{0,1\right\}\subseteq ℝ$$
4	1 2 3	mp2an	$$⊢\left\{0,1\right\}\subseteq ℝ$$