Substitute Two Numbers

Proof: Substitute Two Numbers

Let's prove the following theorem:

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

then a = x + y

Proof:

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

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