Boolean algebra proof - I don't know why this is valid!

Question

So this is the answer proof I was given, I'm stumped by the final application of the Idempotent law (where does that 1 come from!?)

As I understood it a 0 or 1 can only come from a combination of A and not A

R = (A + C) • (A • D + A • D') + A • C + C
R = (A + C) • (A • (D + D')) + A • C + C Distributive Rule
= (A + C) • A + A • C + C Negation Rule
= A • A + C • A + A • C + C Distributive Rule
= A + A • C + C Idempotent Rule
= A • (1 + C) + C Distributive Rule
= A + C Simplification Rule

Answer 1

$$A+A\cdot C = A\cdot 1 + A\cdot C = A\cdot(1+C) $$ since $A\cdot 1=A$, and you're free to use identities "in reverse".