Proof: Subtract Zero Example

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	a - 0 = a + (0 ⋅ (-1))	a - 0 = a + (0 ⋅ (-1)) (Subtraction Property)
2	0 ⋅ (-1) = 0	0 ⋅ (-1) = 0 (Fixed Value Statement)
3	a + (0 ⋅ (-1)) = a + 0	if 0 ⋅ (-1) = 0, then a + (0 ⋅ (-1)) = a + 0 (Substitution)
4	a + 0 = a	a + 0 = a (Additive Identity)
5	a + (0 ⋅ (-1)) = a	if a + (0 ⋅ (-1)) = a + 0 and a + 0 = a, then a + (0 ⋅ (-1)) = a (Transitive Property of Equality)
6	a - 0 = a	if a - 0 = a + (0 ⋅ (-1)) and a + (0 ⋅ (-1)) = a, then a - 0 = a (Transitive Property of Equality)

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