Proof: Substitution in Product

Let's prove the following theorem:

if the following are true:
  • a ⋅ b = c
  • b = d

then a ⋅ d = c

Proof:

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

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