I understand that we can work forwards using logical implications:
If $A \implies B$ and $B \implies C $, then $A \implies C$.
However, I am unsure of the reasoning that allows us to work backwards.
- For instance, If $C \implies D$ and $E \implies C$, then $E \implies D$. Whereas working sequentially forwards with implications seems to make logical sense, I am not sure of the reasoning that makes it logical to work in a 'discontinuous' fashion, as show in the preceding example.
- I am also wondering if, in the preceding example, we could also say that $D \implies E$?
I would greatly appreciate it if someone could please take the time to explain the reasoning behind this concept.