Proof: Substitution in the Middle

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	x + (a + b) = x + c	if a + b = c, then x + (a + b) = x + c (Substitution)
2	(x + a) + b = x + (a + b)	(x + a) + b = x + (a + b) (Associative Property of Addition)
3	(x + a) + b = x + c	if (x + a) + b = x + (a + b) and x + (a + b) = x + c, then (x + a) + b = x + c (Transitive Property of Equality)
4	((x + a) + b) + y = (x + c) + y	if (x + a) + b = x + c, then ((x + a) + b) + y = (x + c) + y (Additive Property of Equality)

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