Proof: Subtract Both Sides Pre 3

Let's prove the following theorem:

if a = b + c, then a + (c ⋅ (-1)) = b + (c + (c ⋅ (-1)))

Proof:

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

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