Theorem sqrt4

Description: The square root of 4 is 2. (Contributed by NM, 3-Aug-1999)

	Ref	Expression
Assertion	sqrt4	$$⊢\sqrt{4}=2$$

Proof

Step	Hyp	Ref	Expression
1		sq2	$$⊢2^2=4$$
2	1	fveq2i	$$⊢\sqrt{2^2}=\sqrt{4}$$
3		2re	$$⊢2\in ℝ$$
4		0le2	$$⊢0\le 2$$
5		sqrtsq	$$⊢\left(2\in ℝ\wedge 0\le 2\right)\to \sqrt{2^2}=2$$
6	3 4 5	mp2an	$$⊢\sqrt{2^2}=2$$
7	2 6	eqtr3i	$$⊢\sqrt{4}=2$$