Is the following a correct logical proof? 
*

*A → (F ∧ P)

*~A → (S ∧ R)

*~R


∴ P


*    assume ~P

*        assume A

*        F ∧ P (1, 5, modus ponens)

*        P (6, simplification)

*    ~A (4, 7, reductio ad absurdum)

*    S ∧ R (2, 8, modus ponens)

*    R (9, simplification)

*P (3, 10, reductio ad absurdum)


The focus for my doubt here is at step 8 where I use the initial assumption at line 4 and the derivation of its negation at line 7 to infer that ~A is in fact the case given the two assumptions. My question is really: am I allowed to use the outer assumption towards negating my inner assumption?
I realize this can also be done by assuming A in the proof and then going from there, I just wanted to make sure this technique is licensed in general.

From
~ A → (S ∧ R),
~(S ∧ R)
→ A
or
((~S) $\lor$ (~R))
→ A.
But we are given ~R.
Therefore A.
