Proof: Subtract From Both Sides

Let's prove the following theorem:

Proof:

Proof Table

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

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