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Metamath Proof Explorer

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	$⊢ \{0, 1\} \subseteq ℝ$

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