Division Theorem
Multiply Both Sides 3
Associative Property of Multiplication 2
Transitive Property of Equality Variation 2
Transitive Property Application 2
Substitution 10
Reorder Terms 7
Reorder Terms 8
Inverse Example

Proof: Substitute Two Variables Theorem

Let's prove the following theorem:

if the following are true:
  • a = x
  • b = y

then a ⋅ b = x ⋅ y

Proof:

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

Given
1 a = x
2 b = y
Proof Table
# Claim Reason
1 a ⋅ b = x ⋅ b if a = x, then a ⋅ b = x ⋅ b
2 x ⋅ b = x ⋅ y if b = y, then x ⋅ b = x ⋅ y
3 a ⋅ b = x ⋅ y if a ⋅ b = x ⋅ b and x ⋅ b = x ⋅ y, then a ⋅ b = x ⋅ y
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