Well, because of the 2 separate tabs, it takes a little effort, but still
doable.
My setup:
Sheet1 and Sheet2, I want to ensure that the dates entered in cells A10:B22
in either sheet are not duplicated.
I inserted 2 helper columns on each sheet before column C.
In cell C10 on sheet 1:
=IF(Sheet2!A10="","",Sheet2!A10)
I then copied down to row 22, and over to column D.
I did the opposite on Sheet2
C10: =IF(Sheet1!A10="","",Sheet1!A10)
copied down, then over.
I hid columns C & D on both sheets.
Then, I selected Sheet1!A10:B22
I go to menu Data | Validation
I chose Custom, and typed the following formula in the formula box
=COUNTIF($A$10:$D$22,A10)<=1
I did the exact same on sheet2.
Note, assuming that when you select your A10:B22 range, that A10 is the
first cell you clicked in, and thus is the active cell. If you selected your
range a different way, be sure to change the cell reference (A10 without the
dollar signs) to whatever is your active cell.