Proof: Multiplicative Property of Equality Variation 2

Let's prove the following theorem:

if a = b, then c ⋅ b = c ⋅ a

Proof:

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Given
1 a = b
Proof Table
# Claim Reason
1 a ⋅ c = b ⋅ c if a = b, then a ⋅ c = b ⋅ c
2 b ⋅ c = c ⋅ b b ⋅ c = c ⋅ b
3 a ⋅ c = c ⋅ b if a ⋅ c = b ⋅ c and b ⋅ c = c ⋅ b, then a ⋅ c = c ⋅ b
4 a ⋅ c = c ⋅ a a ⋅ c = c ⋅ a
5 c ⋅ b = c ⋅ a if a ⋅ c = c ⋅ b and a ⋅ c = c ⋅ a, then c ⋅ b = c ⋅ a

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