Modus ponens and left-nested conditionals (part 2)

Someone told me that (a ⊃ b) ⊃ a and ((a ⊃ b) ⊃ a) ⊃ a together with modus ponens entail a and subsequently b. Is this true? And if yes, could please someone show me how to prove it? (I haven’t found the proof yet).