Equality Example

Transitive Property of Equality Variation 1

Divide Both Sides

Multiply Substitute Two Terms

Multiply Substitute Two Terms 2

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

Distributive Property 2

Commutative Property Variation 1

Distributive Property 3

Associative Property of Multiplication 2

Transitive Property Application 2

Substitution 10

Substitution 12

Divide Simplify 2

Subtract Same Sides

Divide Substitute 2

Divide Substitute 4

Subtract Zero Example

Subtraction Example

Subtract to Zero

Subtract Associative

Midsegment Triangle

Proof: Subtract Associative

Let's prove the following theorem:

(a + b) - c = a + (b - c)

Proof:

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

Proof Table

#	Claim	Reason
1	(a + b) - c = (a + b) + (c ⋅ (-1))	(a + b) - c = (a + b) + (c ⋅ (-1)) (Subtraction Property)
2	(a + b) + (c ⋅ (-1)) = a + (b + (c ⋅ (-1)))	(a + b) + (c ⋅ (-1)) = a + (b + (c ⋅ (-1))) (Associative Property of Addition)
3	b + (c ⋅ (-1)) = b - c	b + (c ⋅ (-1)) = b - c (subtraction_example)
4	a + (b + (c ⋅ (-1))) = a + (b - c)	if b + (c ⋅ (-1)) = b - c, then a + (b + (c ⋅ (-1))) = a + (b - c) (Substitution)
5	(a + b) + (c ⋅ (-1)) = a + (b - c)	if (a + b) + (c ⋅ (-1)) = a + (b + (c ⋅ (-1))) and a + (b + (c ⋅ (-1))) = a + (b - c), then (a + b) + (c ⋅ (-1)) = a + (b - c) (Transitive Property of Equality)
6	(a + b) - c = a + (b - c)	if (a + b) - c = (a + b) + (c ⋅ (-1)) and (a + b) + (c ⋅ (-1)) = a + (b - c), then (a + b) - c = a + (b - c) (Transitive Property of Equality)

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