Transitive Property of Equality Variation 1
Add Associative 2
Transitive Property of Equality Variation 2
Rearrange Sum
Subtract Both Sides
Add Term to Both Sides 6
Reorder Terms 4

Proof: Add Associative 2

Let's prove the following theorem:

(a + b) + c = (a + c) + b

Proof:

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