Proof: Proportion Product

Let's prove the following theorem:

if a / b = c / d, then d ⋅ a = b ⋅ c

Proof:

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Given
1 a / b = c / d
Proof Table
# Claim Reason
1 (b ⋅ d) ⋅ (a / b) = (b ⋅ d) ⋅ (c / d) if a / b = c / d, then (b ⋅ d) ⋅ (a / b) = (b ⋅ d) ⋅ (c / d)
2 (b ⋅ d) ⋅ (a / b) = d ⋅ a (b ⋅ d) ⋅ (a / b) = d ⋅ a
3 (b ⋅ d) ⋅ (c / d) = b ⋅ c (b ⋅ d) ⋅ (c / d) = b ⋅ c
4 d ⋅ a = b ⋅ c if (b ⋅ d) ⋅ (a / b) = (b ⋅ d) ⋅ (c / d) and (b ⋅ d) ⋅ (a / b) = d ⋅ a and (b ⋅ d) ⋅ (c / d) = b ⋅ c, then d ⋅ a = b ⋅ c

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