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Metamath Proof Explorer

Theorem sqrtmsqi

Description: Square root of square. (Contributed by NM, 2-Aug-1999)

Ref Expression
Hypothesis sqrtthi.1 ⊢ 𝐴 ∈ ℝ
Assertion sqrtmsqi ( 0 ≤ 𝐴 → ( √ ‘ ( 𝐴 · 𝐴 ) ) = 𝐴 )

Proof

Step Hyp Ref Expression
1 sqrtthi.1 ⊢ 𝐴 ∈ ℝ
2 sqrtmsq ⊢ ( ( 𝐴 ∈ ℝ ∧ 0 ≤ 𝐴 ) → ( √ ‘ ( 𝐴 · 𝐴 ) ) = 𝐴 )
3 1 2 mpan ⊢ ( 0 ≤ 𝐴 → ( √ ‘ ( 𝐴 · 𝐴 ) ) = 𝐴 )