Step 1: NOT(NOT(a AND b) AND NOT(a AND b)
Step 2: (a AND b) AND (a AND b)
Step 3: a AND b
( NOT(a AND b)) NAND ( NOT(a AND b))
NOT(NOT(a AND b) AND NOT(a AND b))
NOT(NOT(a AND b))
a AND b
(a NAND b) NAND (a NAND b)
=NOT(NOT(a AND b) AND NOT(a AND b))
=(a AND b) AND (a AND b)
=a AND b
=NOT(NOT(a AND b) AND NOT(a AND b))
=NOT(NOT(a AND b))
=a AND b
(a NAND b) NAND (a NAND b)
=(a NOT (a AND b) ) NAND (a NOT (a AND b) )
=(a NOT (a AND b) ) NOT ((a NOT (a AND b) ) AND (a NOT (a AND b) ) )
NOT (a AND b) NAND NOT (a AND b)
NOT NOT( (a AND b) AND (a AND b))
a AND b