Proof: Distributive Property Variation 3

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	(a + b) ⋅ c = (c ⋅ a) + (c ⋅ b)	(a + b) ⋅ c = (c ⋅ a) + (c ⋅ b) (Distributive Property Variation 2)
2	c ⋅ a = a ⋅ c	c ⋅ a = a ⋅ c (Commutative Property of Multiplication)
3	c ⋅ b = b ⋅ c	c ⋅ b = b ⋅ c (Commutative Property of Multiplication)
4	(c ⋅ a) + (c ⋅ b) = (a ⋅ c) + (b ⋅ c)	if c ⋅ a = a ⋅ c and c ⋅ b = b ⋅ c, then (c ⋅ a) + (c ⋅ b) = (a ⋅ c) + (b ⋅ c) (Equality Example)
5	(a + b) ⋅ c = (a ⋅ c) + (b ⋅ c)	if (a + b) ⋅ c = (c ⋅ a) + (c ⋅ b) and (c ⋅ a) + (c ⋅ b) = (a ⋅ c) + (b ⋅ c), then (a + b) ⋅ c = (a ⋅ c) + (b ⋅ c) (Transitive Property of Equality)

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