Commutative Property Variation 1
Substitution 2
Substitution 6
Algebra 4

Proof: Term 1 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 = c + b b + c = c + b
2 a = c + b if a = b + c and b + c = c + b, then a = c + b
3 a = c + d if a = c + b and b = d, then a = c + d
4 c + d = d + c c + d = d + c
5 a = d + c if a = c + d and c + d = d + c, then a = d + c
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