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 3

Let's prove the following theorem:

((b ⋅ 2) + (a ⋅ 2)) / 2 = b + a

Proof:

View as a tree | View dependent proofs | Try proving it

Proof Table

#	Claim	Reason
1	((b ⋅ 2) + (a ⋅ 2)) / 2 = ((b ⋅ 2) + (a ⋅ 2)) ⋅ (1 / 2)	((b ⋅ 2) + (a ⋅ 2)) / 2 = ((b ⋅ 2) + (a ⋅ 2)) ⋅ (1 / 2) (Division is Multiplication by Inverse)
2	((b ⋅ 2) + (a ⋅ 2)) ⋅ (1 / 2) = ((b ⋅ 2) ⋅ (1 / 2)) + ((a ⋅ 2) ⋅ (1 / 2))	((b ⋅ 2) + (a ⋅ 2)) ⋅ (1 / 2) = ((b ⋅ 2) ⋅ (1 / 2)) + ((a ⋅ 2) ⋅ (1 / 2)) (Distributive Property Variation 3)
3	(b ⋅ 2) ⋅ (1 / 2) = b	(b ⋅ 2) ⋅ (1 / 2) = b (simplify_2)
4	(a ⋅ 2) ⋅ (1 / 2) = a	(a ⋅ 2) ⋅ (1 / 2) = a (simplify_2)
5	((b ⋅ 2) + (a ⋅ 2)) ⋅ (1 / 2) = b + ((a ⋅ 2) ⋅ (1 / 2))	if ((b ⋅ 2) + (a ⋅ 2)) ⋅ (1 / 2) = ((b ⋅ 2) ⋅ (1 / 2)) + ((a ⋅ 2) ⋅ (1 / 2)) and (b ⋅ 2) ⋅ (1 / 2) = b, then ((b ⋅ 2) + (a ⋅ 2)) ⋅ (1 / 2) = b + ((a ⋅ 2) ⋅ (1 / 2)) (Term 1 Substitution)
6	((b ⋅ 2) + (a ⋅ 2)) ⋅ (1 / 2) = b + a	if ((b ⋅ 2) + (a ⋅ 2)) ⋅ (1 / 2) = b + ((a ⋅ 2) ⋅ (1 / 2)) and (a ⋅ 2) ⋅ (1 / 2) = a, then ((b ⋅ 2) + (a ⋅ 2)) ⋅ (1 / 2) = b + a (Term 2 Substitution)
7	((b ⋅ 2) + (a ⋅ 2)) / 2 = b + a	if ((b ⋅ 2) + (a ⋅ 2)) / 2 = ((b ⋅ 2) + (a ⋅ 2)) ⋅ (1 / 2) and ((b ⋅ 2) + (a ⋅ 2)) ⋅ (1 / 2) = b + a, then ((b ⋅ 2) + (a ⋅ 2)) / 2 = b + a (Transitive Property of Equality)

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