The proper name of this article is Condorcet//Approval, using the double-slash notation signifying that one eliminates all losers of the first step before performing the second step.
Condorcet//Approval or C//A is a Condorcet method under which one elects the Approval winner when there is no Condorcet winner. Approval could be specified in various ways.
It is also possible to limit contenders to members of the Smith or Schwartz set, resulting in Smith//Approval or Schwartz//Approval.
When approval is implemented such that it isn't possible to rank some candidate X over another candidate Y without also approving candidate X, Condorcet//Approval and similar methods have good burial resistance.