Using AND clause in Arrays/Sumproducts is slightly different, eg:

=MIN(IF(($B$7:$B$15="A")*($F$7:$F$15="Yes"),$G$7:$G$15))
committed with CTRL + SHIFT + ENTER

so in basic syntax terms:

=MIN(IF((test1)*(test2),range))
CSE

or if preferred

=MIN(IF(test1,IF(test2,range)))
CSE

(no need to worry about FALSE condition as the Array will populate with Boolean FALSE as opposed to a number where result of IF not TRUE - and Booleans will be ignored in the MIN test)