My proof for de morgans law

[LogicMaster]

~(A or B) <--> ~A & ~B

(1)

A B
--------(Or Intro) ----------- (Or Intro)
A or B ~(A or B) A or B ~(A or B)
----------------------- (~ Elimination) -----------------------(~E)
absurdity absurdity
------------------------(~ Intro "RAA") ---------------------- (~ Intro)
~A ~B
------------------------------------------------------------------------(& Intro)
~A & ~B
------------------------------------------------------------------------(--> Intro)
~(A or B) --> ~A & ~B

(2)
~A & ~B
----------- (&E "Simplification")
~A A or B ~A & ~B
------------------ (Disjunctive Syllogism) ------------ (&E)
B ~B
------------------------------------------------------------- (~E)
absurdity
--------------- (~I)
~(A or B)
------------------------------(-->I)
~A and ~B --> ~(A or B)

Combining derivations (1) and (2) by (<--> I)
-----------------------------------------------------
~(A or B) <--> ~A & ~B