Proof: Substitution 14

Let's prove the following theorem:

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

then a ⋅ y = b

Proof:

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

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