Multiplicative Property of Equality Variation 1
Substitution 11
Associative Property of Multiplication 2
Transitive Property of Equality Variation 2
Transitive Property Application 2
Substitution 10
Reorder Terms

Proof: First Term Substitution

Let's prove the following theorem:

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

then a = d ⋅ c

Proof:

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