Proof: Distance Symmetry Example 2

Let's prove the following theorem:

if x ⋅ (distance AB) = (distance CD) ⋅ y, then x ⋅ (distance BA) = (distance DC) ⋅ y

Proof:

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Given
1 x ⋅ (distance AB) = (distance CD) ⋅ y
Proof Table
# Claim Reason
1 x ⋅ (distance BA) = (distance CD) ⋅ y if x ⋅ (distance AB) = (distance CD) ⋅ y, then x ⋅ (distance BA) = (distance CD) ⋅ y
2 distance CD = distance DC distance CD = distance DC
3 x ⋅ (distance BA) = (distance DC) ⋅ y if x ⋅ (distance BA) = (distance CD) ⋅ y and distance CD = distance DC, then x ⋅ (distance BA) = (distance DC) ⋅ y
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