Nested IF/And Statement

I received some help yesterday to write an expression to count only results that were in the previous month,

=SUMPRODUCT(--(TEXT(E2:E16,"mm-yy")=TEXT(EOMONTH(TODAY(),-1),"mm-yy")))

Today I'm wondering if I can combine the previous code with the code below using an IF/And nested statement.

=IF($F:$F<3,1,0)

Would it look something like this?

=AND(SUMPRODUCT(--(TEXT($E:$E,"mm-yy")=TEXT(EOMONTH(TODAY(),-1),"mm-yy")))),($F:$F<3,1,0))

I can post a link for the worksheet if you need, but just looking to combine those two criteria into one.