Transitive Property of Equality Variation 2
Multiplication Property 2
Multiplicative Property of Equality Variation 1
Associative Property of Multiplication 2
Transitive Property Application 2
Substitution 10
Reordering Terms Theorem
Multiplicative Identity 3
Division Theorem
Substitution 11
Substitution 14
Multiplication Property 3
Reorder Terms
Reduction Property
Cross Multiply Theorem
Substitution 12
Substitution in Product
Distance Symmetry Example 5
Distance Symmetry Example 2
Equality Example
Distance Algebra Example

Proof: Substitution 12

Let's prove the following theorem:

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

then a = b ⋅ d

Proof:

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

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