Substitute 12

Proof: Substitute 12

Let's prove the following theorem:

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

then a ⋅ c = d

Proof:

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

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