Proof: Subtract Both Sides 3

Let's prove the following theorem:

if a = b, then a - c = b - c

Proof:

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

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