XL interprets any non-zero numeric value as TRUE and zero as FALSE, so,
literally:
=IF(AND(A1<>0,B1<>0),A1+B1,"Something else")
OTOH, XL coerces TRUE to 1 in math formulae and FALSE to 0, so "if A1 is
true then B1 is also true" translates to
B1: =IF(A1=TRUE, TRUE, "Something Else")
and
result = IF(A1=TRUE, A1+B1,"Something Else Again")
which will always return 2 (TRUE+TRUE===> 1+1).