Midpoint Sum
Commutative Property Example 2
Commutative Property Variation 1
Substitution 2
Substitution 8
Substitution Example 10
Substitute 2
Multiplicative Identity 2
Distributive Property 4
Multiplicative Property of Equality Variation 1
Addition Theorem
Transitive Property of Equality Variation 2
Associative Property of Multiplication 2
Transitive Property Application 2
Substitution 10
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
Substitution 12
Divide Simplify 2
Simplify 2
Multiply by 2
Midpoint Theorem

Proof: Substitute 2

Let's prove the following theorem:

if the following are true:
  • a + b = c
  • d = b

then a + d = c

Proof:

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

Given
1 a + b = c
2 d = b
Proof Table
# Claim Reason
1 b = d if d = b, then b = d
2 a + d = c if a + b = c and b = d, then a + d = c
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