Proof: Double Transitive Property Less 2

Let's prove the following theorem:

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

then x < y

Proof:

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

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