Proof: Sum Equation

Let's prove the following theorem:

if (a + b) + c = d, then a + c = d - b

Proof:

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

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