Proof: Add Term to Both Sides 5

Let's prove the following theorem:

if a + b = c, then b = c + (a ⋅ (-1))

Proof:

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

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