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Metamath Proof Explorer

Theorem sqrt2re

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

		Ref	Expression
	Assertion	sqrt2re	⊢ ( √ ‘ 2 ) ∈ ℝ

Step	Hyp	Ref	Expression
1		2re	⊢ 2 ∈ ℝ
2		2pos	⊢ 0 < 2
3	1 2	sqrtpclii	⊢ ( √ ‘ 2 ) ∈ ℝ