Theorem 1. Cancellation Law for Addition.
If a + b = b + c , then b = c
Theorem 2. Possibility of Subteation .
Given a and b , there exactly one x s.t. a + x = b
Theorem 3. b - a = b + ( -a )
Theorem 4. - (-a) = a
Theorem 5. a( b - c ) = ab - ac
Theorem 6. 0*a = a*0 = 0
Theorem 7. Cancellation of Mutiplication .
If ab = ac and a ≠ 0 , then b = c
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