Transitive Property of Equality Variation 1
Divide Both Sides
Transitive Property of Equality Variation 2
Substitution 2

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:

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Given
1 a / b = c / d
2 a = w
3 b = x
4 d = z
Proof Table
# 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 w / b = w / x and a / b = w / b, then a / b = w / x
4 w / x = c / d if a / b = c / d and a / b = w / x, then w / x = c / d
5 c / d = c / z if d = z, then c / d = c / z
6 w / x = c / z if c / d = c / z and w / x = c / d, then w / x = c / z
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