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