The Sufficient Condition for an Analytic Function ( for C-R Equations ).

State and prove that:
The Sufficient condition for an Analytic Function.
Or
Statement/Prove that: w= f(z) = u + iv is analytic in a domain D and if
(i) u, v are differentiable in domain D and
ux = vy; uy = -vx
(ii) These are partial derivatives ux, vx, uy and vy all are continuous in D.
(here x,y is in Subscript)
Proof:
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