1. (Q ⊃ ~J) ⊃ (M ⊃ ~D)
2. Q ⊃ M
3. M ⊃ ~J            /Q ⊃ ~D

4. Q ⊃ ~J       2,3, Hypothetical Syllogism | Must Learn:[(p⊃q)&(q⊃r)]⊃(p⊃r)
5. M ⊃ ~D       1,4, Modus Ponens           | Must learn:[(p⊃q)&p]⊃q

It's common sense that if the first thing implies the second thing, and the
second thing implies the third thing, then the first thing implies the third
thing. That's hypothetical syllogism.

It's common sense that if the first thing implies the second thing, and you know
the first thing is true, then you know the second thing is also true. That's
modus ponens.

Logic is plain old common sense.  You just have to learn how to read it, and
the names for the bits of common sense.

Edwin