reserve q,th,r for Real,
  a,b,p for Real,
  w,z for Complex,
  k,l,m,n,n1,n2 for Nat,
  seq,seq1,seq2,cq1 for Complex_Sequence,
  rseq,rseq1,rseq2 for Real_Sequence,
  rr for set,
  hy1 for 0-convergent non-zero Real_Sequence;
reserve d for Real;
reserve th,th1,th2 for Real;

theorem Th65:
  exp_R is_differentiable_on REAL & diff(exp_R,th)=exp_R.th
proof
A1: [#]REAL is open Subset of REAL & REAL c=dom exp_R by FUNCT_2:def 1;
 for r st r in REAL holds exp_R is_differentiable_in r by Th64;
  hence thesis by A1,Th64,FDIFF_1:9;
end;
