Proof: Multiplication Substitution

Let's prove the following theorem:

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

then c = a ⋅ b

Proof:

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

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