Associative
Transitive Property of Equality Variation 2
Simplify 4

Proof: Simplify 4

Let's prove the following theorem:

(a + b) + (b ⋅ (-1)) = a

Proof:

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Proof Table
# Claim Reason
1 b + (b ⋅ (-1)) = 0 b + (b ⋅ (-1)) = 0
2 a + (b + (b ⋅ (-1))) = a + 0 if b + (b ⋅ (-1)) = 0, then a + (b + (b ⋅ (-1))) = a + 0
3 a + 0 = a a + 0 = a
4 a + (b + (b ⋅ (-1))) = a if a + (b + (b ⋅ (-1))) = a + 0 and a + 0 = a, then a + (b + (b ⋅ (-1))) = a
5 a + (b + (b ⋅ (-1))) = (a + b) + (b ⋅ (-1)) a + (b + (b ⋅ (-1))) = (a + b) + (b ⋅ (-1))
6 (a + b) + (b ⋅ (-1)) = a if a + (b + (b ⋅ (-1))) = (a + b) + (b ⋅ (-1)) and a + (b + (b ⋅ (-1))) = a, then (a + b) + (b ⋅ (-1)) = a
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