Rules of inference - Is my application of simplification in this proof, correct?

Question

Could someone verify that my proof is valid as the question did not have a solution?

1. $(\lnot R \lor \lnot F) \to (S \land L)$
   
2. $(S \to T)$
   
3. $(\lnot T)$
   
4. $(\lnot S)$ 2,3 Modus tollens
   
5. $\lnot (\lnot R \lor \lnot F) \lor (S \land L)$ 1, implication equivalence
   
6. $(R \land F) \lor (S \land L)$ 5, double negation
   
7. $(R \lor S)$ 6, simplification
   
8. $(R)$ 7,4 Disjunctive syllogism
   

My main concern is with line 7 with the use of simplification, have I applied the rule correctly?
I understand that with simplification if you have $(P \land Q)$ and apply it, it returns $(P)$.

For my proof, you had to show that lines 1-3 (the hypotheses) entail $R$.

Answer 1

As correctly said by Mauro Allegranza, your usage of simplification is wrong.

As an alternative to the proofs suggested by Mauro Allegranza (which are perfect), consider the following proof:

1. $(\lnot R \lor \lnot F) \to (S \land L)$ assumption
2. $(S \to T)$ assumption
3. $(\lnot T)$ assumption
4. $(\lnot S)$ 2,3 Modus tollens
5. $(\lnot S \lor \lnot L)$ 4, addition
6. $\lnot(S \land L)$ 5, De Morgan
7. $\lnot(\lnot R \lor \lnot F)$ 1, 6 Modus tollens
8. $(R \land F)$ 7, double negation (De Morgan)
9. $(R)$ 8, simplification