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You get an increase in the Standard Deduction on 1040 line 40.  

Joint Standard Deduction is $12,600
and you get an extra $1,250 for each spouse 65+
So one person over 65 would give you $13,850

Or you take your Itemized Deductions, whichever is more.  If you itemize you don't get any credit for being 65 or older.