Summing Range based on Criteria of Two Other Ranges

I have a fairly large Sheet with data similar to below where I've labeled the columns A-D.
What I'm trying to do is Sum the values in Column A for each unique value in Column B AND in Column C, then show those values as new Columns (E) and (F).

In my example, I added all of the values in Column A that equal "IF" in Column B (AND) had a value of "1" in Column C...and placed that in column F. This is the value I'm trying to obtain for any given range.

Column E is just the unique value of Column B value appended with Column C value. Column F is the sum of column A.

HTML Code: 

Does anyone have an idea of how I can do this?

The values you put there in column E (IF1 IF2 TE2)
Are those all in one cell?

Try

=SUMIFS(A$1:A$100,B$1:B$100,LEFT(E1,2),C$1:C$100,RIGHT(E1,1)+0)

E1 = IF1

Alkey, your solution worked perfect!
I always seem to over complicate things.
Thank you so much.