Commutative Property Variation 1
Substitution 2
Subtraction Example
Transitive Property of Equality Variation 2
Transitive Property Application 2
Subtract Substitute 2 Vars

Proof: Term 2 Substitution

Let's prove the following theorem:

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

then a = b + d

Proof:

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