Proof: Algebra One

Let's prove the following theorem:

if the following are true:
  • a = 1
  • a ⋅ a = b

then 1 = b

Proof:

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Given
1 a = 1
2 a ⋅ a = b
Proof Table
# Claim Reason
1 a ⋅ a = 1 ⋅ a if a = 1, then a ⋅ a = 1 ⋅ a
2 1 ⋅ a = 1 ⋅ 1 if a = 1, then 1 ⋅ a = 1 ⋅ 1
3 1 ⋅ 1 = b if a ⋅ a = 1 ⋅ a and 1 ⋅ a = 1 ⋅ 1 and a ⋅ a = b, then 1 ⋅ 1 = b
4 1 ⋅ 1 = 1 1 ⋅ 1 = 1
5 1 = b if 1 ⋅ 1 = 1 and 1 ⋅ 1 = b, then 1 = b

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