reserve A for QC-alphabet;
reserve X,T for Subset of CQC-WFF(A);
reserve F,G,H,p,q,r,t for Element of CQC-WFF(A);
reserve s,h for QC-formula of A;
reserve x,y for bound_QC-variable of A;
reserve f for FinSequence of [:CQC-WFF(A),Proof_Step_Kinds:];
reserve i,j for Element of NAT;

theorem Th62:
  Ex(x,p => q) <=> (All(x,p) => Ex(x,q)) is valid
proof
  Ex(x,p => q) => (All(x,p) => Ex(x,q)) is valid & (All(x,p) => Ex(x,q))
  => Ex (x,p => q) is valid by Th61;
  hence thesis by Lm14;
end;
