Proof: Substitution 7

Let's prove the following theorem:

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

then a = d + c

Proof:

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

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