Strengthening the Antecedent: From B implies C, infer (A ^ B) implies C

Question

How can I construct a Fitch style proof to prove this? I have tried

1. B $\rightarrow$ C
   2. A $\land$ B
   3. B $\quad\quad$ $\land$ Elim: $2$
   4. C $\quad\quad$ $\rightarrow$ Elim: $1,3$

$5$. (A $\land$ B) $\rightarrow$ C $\quad\quad$ $\rightarrow$ Intro: $2-4$

Answer 1

You may want to indicate what kind of Elim and Intro you do:

Line 3 is an $\land$ Elim

Line4 is an $\rightarrow$ Elim

line 5 is an $\rightarrow $ Intro

Otherwise perfect!

Answer 2

So far, so good. You have only one more line to add to complete your proof: $(B\implies C) \implies ((A\land B) \implies C)$.