Suppose the problem is that given $A$ and $C$ holds, prove $D$ holds.
Some theorems that we can use are:
$A \to B$
$(B,C) \to D$
I feel what I said may be unclear:
Because $A$ holds and $A$ implies $B$, $B$ holds. Because $B$ and $C$ holds and $B$ and $C$ imply $D$, $D$ holds.
Usually $A$, $B$, $C$ and $D$ are long sentences and may contain "and" again.
Also there sometimes can be more conditions and theorems for proving $D$.
In all of these cases, the above quote can be very long and I am afraid may be confusing.
How would you write it?
Do you mainly use words or formulas?