Subtraction Example
Transitive Property of Equality Variation 2
Subtract to Zero
Transitive Property of Equality Variation 1
Divide Both Sides
Subtract Associative
Subtract 1
Divide Zero 2

Proof: Divide Zero 2

Let's prove the following theorem:

if b > 0, then (c - c) / ((b + a) - a) = 0

Proof:

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Given
1 b > 0
Proof Table
# Claim Reason
1 not (b = 0) if b > 0, then not (b = 0)
2 c - c = 0 c - c = 0
3 (c - c) / b = 0 / b if c - c = 0, then (c - c) / b = 0 / b
4 0 / b = 0 if not (b = 0), then 0 / b = 0
5 (c - c) / b = 0 if (c - c) / b = 0 / b and 0 / b = 0, then (c - c) / b = 0
6 (b + a) - a = b (b + a) - a = b
7 (c - c) / ((b + a) - a) = (c - c) / b if (b + a) - a = b, then (c - c) / ((b + a) - a) = (c - c) / b
8 (c - c) / ((b + a) - a) = 0 if (c - c) / ((b + a) - a) = (c - c) / b and (c - c) / b = 0, then (c - c) / ((b + a) - a) = 0
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