Proof: Add Term to Both Sides

Let's prove the following theorem:

if a = b, then c + a = c + b

Proof:

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

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