Proof: Substitute Two Terms

Let's prove the following theorem:

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

then f = b - d

Proof:

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

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