Proof: Subtract Both Sides

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	a + (c ⋅ (-1)) = b + (c + (c ⋅ (-1)))	if a = b + c, then a + (c ⋅ (-1)) = b + (c + (c ⋅ (-1))) (Subtract Both Sides Pre 3)
2	b + (c + (c ⋅ (-1))) = b	b + (c + (c ⋅ (-1))) = b (subtract_both_sides_pre_2)
3	a + (c ⋅ (-1)) = b	if a + (c ⋅ (-1)) = b + (c + (c ⋅ (-1))) and b + (c + (c ⋅ (-1))) = b, then a + (c ⋅ (-1)) = b (Transitive Property of Equality)

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