Proof: Substitution 8
Let's prove the following theorem:
if the following are true:
- a + b = c
- a = d
then d + b = c
Proof:
Given
| 1 | a + b = c |
|---|---|
| 2 | a = d |
| # | Claim | Reason |
|---|---|---|
| 1 | b + a = c | if a + b = c, then b + a = c |
| 2 | c = b + a | if b + a = c, then c = b + a |
| 3 | c = b + d | if c = b + a and a = d, then c = b + d |
| 4 | b + d = d + b | b + d = d + b |
| 5 | c = d + b | if c = b + d and b + d = d + b, then c = d + b |
| 6 | d + b = c | if c = d + b, then d + b = c |
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