Proof: Sum Equation

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	a + b = b + a	a + b = b + a (Commutative Property of Addition)
2	(b + a) + c = d	if (a + b) + c = d and a + b = b + a, then (b + a) + c = d (Substitution 8)
3	a + c = d + (b ⋅ (-1))	if (b + a) + c = d, then a + c = d + (b ⋅ (-1)) (Add Term to Both Sides 4)
4	d - b = d + (b ⋅ (-1))	d - b = d + (b ⋅ (-1)) (Subtraction Property)
5	a + c = d - b	if a + c = d + (b ⋅ (-1)) and d - b = d + (b ⋅ (-1)), then a + c = d - b (Transitive Property of Equality Variation 1)

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