boundedness law in a boolean algebra

Show that a +1 = 1 in a boolean algebra

1 = a + a'
= a + (a' .1 )
= (a + a' ) . ( a+1) distributive law
= 1 . ( a+1)
=a +1

therefore a + 1 = 1

note that the dual is a . 0 = 0

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