How do I dependency inject providers using MEF?

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C#

MEF

I thought it would be possible to write the following code:

[Export]
public class ClassA
{
}

public class ClassB
{
  private readonly Func<ClassA> classAProvider;

  [ImportingConstructor]
  public ClassB(Func<ClassA> classAProvider)
  {
    this.classAProvider = classAProvider;
  }

  public ClassA CreateClassA()
  {
    return classAProvider();
  }
}

Can you please help me figure out how I can inject a provider for ClassA into ClassB? I have noticed ExportFactory, but I don't like the fact that I have to dispose it.