Theorem sqrt1

Description: The square root of 1 is 1. (Contributed by NM, 31-Jul-1999)

	Ref	Expression
Assertion	sqrt1	⊢ ( √ ‘ 1 ) = 1

Proof

Step	Hyp	Ref	Expression
1		sq1	⊢ ( 1 ↑ 2 ) = 1
2	1	fveq2i	⊢ ( √ ‘ ( 1 ↑ 2 ) ) = ( √ ‘ 1 )
3		1re	⊢ 1 ∈ ℝ
4		0le1	⊢ 0 ≤ 1
5		sqrtsq	⊢ ( ( 1 ∈ ℝ ∧ 0 ≤ 1 ) → ( √ ‘ ( 1 ↑ 2 ) ) = 1 )
6	3 4 5	mp2an	⊢ ( √ ‘ ( 1 ↑ 2 ) ) = 1
7	2 6	eqtr3i	⊢ ( √ ‘ 1 ) = 1