Proof: Substitution 12

Let's prove the following theorem:

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

then a = b ⋅ d

Proof:

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

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