Proof: Simplify If

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	(((-1) ⋅ 3) ⋅ x) + ((3 ⋅ x) + 20) = (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x)	if (3 ⋅ x) + 20 = 4 ⋅ x, then (((-1) ⋅ 3) ⋅ x) + ((3 ⋅ x) + 20) = (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) (Substitution)
2	(((-1) ⋅ 3) ⋅ x) + ((3 ⋅ x) + 20) = 20	(((-1) ⋅ 3) ⋅ x) + ((3 ⋅ x) + 20) = 20 (simplify_4)
3	20 = (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x)	if (((-1) ⋅ 3) ⋅ x) + ((3 ⋅ x) + 20) = 20 and (((-1) ⋅ 3) ⋅ x) + ((3 ⋅ x) + 20) = (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x), then 20 = (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) (Transitive Property of Equality Variation 2)
4	(((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) = x	(((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) = x (simplify_5)
5	20 = x	if 20 = (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) and (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) = x, then 20 = x (Transitive Property of Equality)

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