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Metamath Proof Explorer

Theorem sqr00d

Description: A square root is zero iff its argument is 0. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypotheses abscld.1 ⊢ φ → A ∈ ℂ
sqrt00d.2 ⊢ φ → A = 0
Assertion sqr00d ⊢ φ → A = 0

Proof

Step Hyp Ref Expression
1 abscld.1 ⊢ φ → A ∈ ℂ
2 sqrt00d.2 ⊢ φ → A = 0
3 1 sqsqrtd ⊢ φ → A 2 = A
4 2 sq0id ⊢ φ → A 2 = 0
5 3 4 eqtr3d ⊢ φ → A = 0