Proof: Multiply Both Sides 2
Let's prove the following theorem:
if a = b / c, then c ⋅ a = b
Proof:
Given
| 1 | a = b / c |
|---|
| # | Claim | Reason |
|---|---|---|
| 1 | a ⋅ c = (b / c) ⋅ c | if a = b / c, then a ⋅ c = (b / c) ⋅ c |
| 2 | (b / c) ⋅ c = b | (b / c) ⋅ c = b |
| 3 | a ⋅ c = b | if a ⋅ c = (b / c) ⋅ c and (b / c) ⋅ c = b, then a ⋅ c = b |
| 4 | a ⋅ c = c ⋅ a | a ⋅ c = c ⋅ a |
| 5 | c ⋅ a = b | if a ⋅ c = c ⋅ a and a ⋅ c = b, then c ⋅ a = b |
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