Proof: Multiply By 1 Theorem

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	(1 / c) ⋅ c = 1	(1 / c) ⋅ c = 1 (Inverse Product Theorem)
2	((1 / c) ⋅ c) ⋅ b = 1 ⋅ b	if (1 / c) ⋅ c = 1, then ((1 / c) ⋅ c) ⋅ b = 1 ⋅ b (Multiplicative Property of Equality)
3	((1 / c) ⋅ c) ⋅ b = (b ⋅ (1 / c)) ⋅ c	((1 / c) ⋅ c) ⋅ b = (b ⋅ (1 / c)) ⋅ c (reordering_terms_theorem)
4	(b ⋅ (1 / c)) ⋅ c = 1 ⋅ b	if ((1 / c) ⋅ c) ⋅ b = (b ⋅ (1 / c)) ⋅ c and ((1 / c) ⋅ c) ⋅ b = 1 ⋅ b, then (b ⋅ (1 / c)) ⋅ c = 1 ⋅ b (Transitive Property of Equality Variation 2)
5	1 ⋅ b = b	1 ⋅ b = b (multiplicative_identity_3)
6	(b ⋅ (1 / c)) ⋅ c = b	if (b ⋅ (1 / c)) ⋅ c = 1 ⋅ b and 1 ⋅ b = b, then (b ⋅ (1 / c)) ⋅ c = b (Transitive Property of Equality)
7	b ⋅ (1 / c) = b / c	b ⋅ (1 / c) = b / c (division_theorem)
8	(b / c) ⋅ c = b	if b ⋅ (1 / c) = b / c and (b ⋅ (1 / c)) ⋅ c = b, then (b / c) ⋅ c = b (Substitution 14)

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