Substitution 11
Substitution 14
Multiplicative Property of Equality Variation 1
Substitution 12
Substitution in Product
Commutative Property Variation 1
Substitution 2
Substitution 6
Algebra Substitution

Proof: Substitution 14

Let's prove the following theorem:

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

then a ⋅ y = b

Proof:

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

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