Proof: Add Terms Twice

Let's prove the following theorem:

if x = y, then (a + x) + c = (a + y) + c

Proof:

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Given
1 x = y
Proof Table
# Claim Reason
1 a + x = a + y if x = y, then a + x = a + y
2 (a + x) + c = (a + y) + c if a + x = a + y, then (a + x) + c = (a + y) + c

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