Proof: Swap 2 and 3 Theorem

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	b ⋅ c = c ⋅ b	b ⋅ c = c ⋅ b (Commutative Property of Multiplication)
2	a ⋅ (b ⋅ c) = a ⋅ (c ⋅ b)	if b ⋅ c = c ⋅ b, then a ⋅ (b ⋅ c) = a ⋅ (c ⋅ b) (Multiplicative Property of Equality Variation 1)
3	a ⋅ (b ⋅ c) = (a ⋅ b) ⋅ c	a ⋅ (b ⋅ c) = (a ⋅ b) ⋅ c (associative_property_of_multiplication_2)
4	a ⋅ (c ⋅ b) = (a ⋅ c) ⋅ b	a ⋅ (c ⋅ b) = (a ⋅ c) ⋅ b (associative_property_of_multiplication_2)
5	(a ⋅ b) ⋅ c = (a ⋅ c) ⋅ b	if a ⋅ (b ⋅ c) = a ⋅ (c ⋅ b) and a ⋅ (b ⋅ c) = (a ⋅ b) ⋅ c and a ⋅ (c ⋅ b) = (a ⋅ c) ⋅ b, then (a ⋅ b) ⋅ c = (a ⋅ c) ⋅ b (Transitive Property Application 2)

Comments

Please log in to add comments