Theorem sqrt4

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

	Ref	Expression
Assertion	sqrt4	⊢ ( √ ‘ 4 ) = 2

Proof

Step	Hyp	Ref	Expression
1		sq2	⊢ ( 2 ↑ 2 ) = 4
2	1	fveq2i	⊢ ( √ ‘ ( 2 ↑ 2 ) ) = ( √ ‘ 4 )
3		2re	⊢ 2 ∈ ℝ
4		0le2	⊢ 0 ≤ 2
5		sqrtsq	⊢ ( ( 2 ∈ ℝ ∧ 0 ≤ 2 ) → ( √ ‘ ( 2 ↑ 2 ) ) = 2 )
6	3 4 5	mp2an	⊢ ( √ ‘ ( 2 ↑ 2 ) ) = 2
7	2 6	eqtr3i	⊢ ( √ ‘ 4 ) = 2