Commutative Property Variation 1
Substitution 2
Substitution 6
Algebra2

Proof: Algebra2

Let's prove the following theorem:

if the following are true:
  • a = ((b + c) + d) + e
  • b = x + y

then a = (((x + y) + c) + d) + e

Proof:

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Given
1 a = ((b + c) + d) + e
2 b = x + y
Proof Table
# Claim Reason
1 b + c = (x + y) + c if b = x + y, then b + c = (x + y) + c
2 (b + c) + d = ((x + y) + c) + d if b + c = (x + y) + c, then (b + c) + d = ((x + y) + c) + d
3 a = (((x + y) + c) + d) + e if a = ((b + c) + d) + e and (b + c) + d = ((x + y) + c) + d, then a = (((x + y) + c) + d) + e
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