Metamath Proof Explorer

Theorem sqsqrtd

Description: Square root theorem. Theorem I.35 of Apostol p. 29. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypothesis abscld.1 
|- ( ph -> A e. CC )
Assertion sqsqrtd 
|- ( ph -> ( ( sqrt ` A ) ^ 2 ) = A )

Proof

Step Hyp Ref Expression
1 abscld.1 
 |-  ( ph -> A e. CC )
2 sqrtth 
 |-  ( A e. CC -> ( ( sqrt ` A ) ^ 2 ) = A )
3 1 2 syl 
 |-  ( ph -> ( ( sqrt ` A ) ^ 2 ) = A )