sum, if column contains array of specific strings

Dear Forum,

I have the following issue: I want to test whether the letters in Column A are also in Column C (refer to the table below). If so, sum the values in Column B that are associated with Column A. In the example below this should return 2, since from column A only the letters F and G also occur in Column C and F is associated with 2 and G with 0. I tried {=SUMIF(A2:A5;C2:C4;B2:B5)}, which returns the false value 0 since the the Fs in Columns A and C are not in the same row (and I cannot change the dataset to make this the case).
Do you know any formula that can do this operation?

Any help is very much appreciated.

Best regards,
Mag2

	A	B	C
1	letters to be tested	values associated with ColA	letters to be tested against
2	F	2	X
3	G		F
4	H	3	G
5	I