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Default match in multi-column and multi-row array

I have a dataset that consists of 4 full columns of data. On another
sheet I have a list of values (1000 values in column A.) I would like
to search in the dataset for an exact match with each value in my list
returning TRUE if there's a match and FALSE if there's no match (1
return value in column B for each original list value in column A.)

Is there a way to do this without using 4 vlookups? In addition, to
simplifying the formula, is there a way to do this using a formula that
doesn't take as long to calculate?

 
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