Theorem sqrt2re

Description: The square root of 2 exists and is a real number. (Contributed by NM, 3-Dec-2004)

	Ref	Expression
Assertion	sqrt2re	$$⊢\sqrt{2}\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		2re	$$⊢2\in ℝ$$
2		2pos	$$⊢0<2$$
3	1 2	sqrtpclii	$$⊢\sqrt{2}\in ℝ$$