Computer Science boolean expression question

The method for simplifying this boolean expression is given

(¬A∨B)∧¬(A∨¬(B∨A))
=(¬A∨B)∧(¬A∧(B∨A))
=(¬A∨B)∧(¬A∧B∨¬A∧A)
=(¬A∨B)∧(¬A∧B)
=¬A∧¬A∧B∨B∧¬A∧B
=¬A∧B∨¬A∧B
=¬A∧B

The task is to order the identities/laws that were used in the correct order. I've put them as

De Morgan's law
distributive law
use of identities X AND NOT X = 0 and X OR 0 = X
distributive law
use of identity X AND X = X [twice]
use of identity X OR X = X

(I wasn't sure of the last one but it was the only one left over) I don't know what I've done wrong. Help? Thanks :smile:

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