Multiplicative Identity 2
Commutative Property Variation 1
Substitution 2
Distributive Property 4
Multiplicative Property of Equality Variation 1
Addition Theorem
Transitive Property of Equality Variation 2
Transitive Property of Equality Variation 1
Divide Both Sides
Multiplicative Property of Equality Variation 2
Transitive Property of Equality Variation 3
Division is Commutative
Associative Property
Divide Each Side
Divide 180 by 2 2
One Eighty 4

Proof: Addition Theorem

Let's prove the following theorem:

a + a = a ⋅ 2

Proof:

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Proof Table
# Claim Reason
1 a ⋅ 1 = a a ⋅ 1 = a
2 (a ⋅ 1) + a = a + a if a ⋅ 1 = a, then (a ⋅ 1) + a = a + a
3 a + a = (a ⋅ 1) + a if (a ⋅ 1) + a = a + a, then a + a = (a ⋅ 1) + a
4 a = a ⋅ 1 a = a ⋅ 1
5 a + a = (a ⋅ 1) + (a ⋅ 1) if a + a = (a ⋅ 1) + a and a = a ⋅ 1, then a + a = (a ⋅ 1) + (a ⋅ 1)
6 (a ⋅ 1) + (a ⋅ 1) = a ⋅ (1 + 1) (a ⋅ 1) + (a ⋅ 1) = a ⋅ (1 + 1)
7 1 + 1 = 2 1 + 1 = 2
8 a ⋅ (1 + 1) = a ⋅ 2 if 1 + 1 = 2, then a ⋅ (1 + 1) = a ⋅ 2
9 (a ⋅ 1) + (a ⋅ 1) = a ⋅ 2 if (a ⋅ 1) + (a ⋅ 1) = a ⋅ (1 + 1) and a ⋅ (1 + 1) = a ⋅ 2, then (a ⋅ 1) + (a ⋅ 1) = a ⋅ 2
10 a + a = a ⋅ 2 if a + a = (a ⋅ 1) + (a ⋅ 1) and (a ⋅ 1) + (a ⋅ 1) = a ⋅ 2, then a + a = a ⋅ 2
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