Subtraction Example
Subtract Associative

Proof: Subtract Associative

Let's prove the following theorem:

(a + b) - c = a + (b - c)

Proof:

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Proof Table
# Claim Reason
1 (a + b) - c = (a + b) + (c ⋅ (-1)) (a + b) - c = (a + b) + (c ⋅ (-1))
2 (a + b) + (c ⋅ (-1)) = a + (b + (c ⋅ (-1))) (a + b) + (c ⋅ (-1)) = a + (b + (c ⋅ (-1)))
3 b + (c ⋅ (-1)) = b - c b + (c ⋅ (-1)) = b - c
4 a + (b + (c ⋅ (-1))) = a + (b - c) if b + (c ⋅ (-1)) = b - c, then a + (b + (c ⋅ (-1))) = a + (b - c)
5 (a + b) + (c ⋅ (-1)) = a + (b - c) if (a + b) + (c ⋅ (-1)) = a + (b + (c ⋅ (-1))) and a + (b + (c ⋅ (-1))) = a + (b - c), then (a + b) + (c ⋅ (-1)) = a + (b - c)
6 (a + b) - c = a + (b - c) if (a + b) - c = (a + b) + (c ⋅ (-1)) and (a + b) + (c ⋅ (-1)) = a + (b - c), then (a + b) - c = a + (b - c)
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