Law of Conservation of Energy :Energy can neither be created nor be destroyed.

Law of Conservation of Mechanical Energy: It states that  mechanical energy of a system always remains conserved if work done by conservative forces is zero.

Accrording to Work Energy Theorem

W_all = ∆K

W_nc   + W_c  = ∆K

 If work done by all the conservative forces is zero i.e. W_nc = 0

W_c= ∆K

And Also W_c   =  -∆U

So

-∆U=∆K

-(U_f  - U_i  ) = K_f – K_i

K_i    +  U_i =K_f   + U_f

Initial Mechanical  Energy  = Final Mechanical Energy