Proof: Multiply by One

Let's prove the following theorem:

(a ⋅ (1 / c)) ⋅ c = a

Proof:

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

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