Proof: Multiplicative Property of Equality Variation 1

Let's prove the following theorem:

if a = b, then c ⋅ a = c ⋅ b

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 c ⋅ a = a ⋅ c c ⋅ a = a ⋅ c
5 c ⋅ a = c ⋅ b if c ⋅ a = a ⋅ c and a ⋅ c = c ⋅ b, then c ⋅ a = c ⋅ b

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