Equality Example
Transitive Property of Equality Variation 1
Divide Both Sides
Multiply Substitute Two Terms
Multiply Substitute Two Terms 2
Zero Plus a
Transitive Property of Equality Variation 2
Multiplicative Property of Equality Variation 2
Transitive Property of Equality Variation 3
Division is Commutative
Associative Property
Multiplicative Property of Equality Variation 1
Simplify
Transitive
Distributive Property 2
Commutative Property Variation 1
Substitution 2
Substitution 6
Distributive Property 3
Associative Property of Multiplication 2
Transitive Property Application 2
Substitution 10
Substitution 12
Divide Simplify 2
Simplify 2
Simplify 3
Transitive 2
Subtract Same Sides
Divide Both
Divide Substitute 2
Divide Substitute 4
Slope 1
Subtract Zero Example
Subtraction Example
Subtract to Zero
Example 2
Subtract Associative
Subtract 1
Divide Zero 2
Midsegment Triangle

Proof: Simplify

Let's prove the following theorem:

(0 + (a ⋅ 2)) / 2 = a

Proof:

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Proof Table
# Claim Reason
1 0 + (a ⋅ 2) = a ⋅ 2 0 + (a ⋅ 2) = a ⋅ 2
2 (0 + (a ⋅ 2)) / 2 = (a ⋅ 2) / 2 if 0 + (a ⋅ 2) = a ⋅ 2, then (0 + (a ⋅ 2)) / 2 = (a ⋅ 2) / 2
3 (a ⋅ 2) / 2 = a ⋅ (2 / 2) (a ⋅ 2) / 2 = a ⋅ (2 / 2)
4 2 / 2 = 1 2 / 2 = 1
5 a ⋅ (2 / 2) = a ⋅ 1 if 2 / 2 = 1, then a ⋅ (2 / 2) = a ⋅ 1
6 a ⋅ 1 = a a ⋅ 1 = a
7 a ⋅ (2 / 2) = a if a ⋅ (2 / 2) = a ⋅ 1 and a ⋅ 1 = a, then a ⋅ (2 / 2) = a
8 (a ⋅ 2) / 2 = a if (a ⋅ 2) / 2 = a ⋅ (2 / 2) and a ⋅ (2 / 2) = a, then (a ⋅ 2) / 2 = a
9 (0 + (a ⋅ 2)) / 2 = a if (0 + (a ⋅ 2)) / 2 = (a ⋅ 2) / 2 and (a ⋅ 2) / 2 = a, then (0 + (a ⋅ 2)) / 2 = a
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