Proof: Simplify If

Let's prove the following theorem:

if (3 ⋅ x) + 20 = 4 ⋅ x, then 20 = x

Proof:

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Given
1 (3 ⋅ x) + 20 = 4 ⋅ x
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)
2 (((-1) ⋅ 3) ⋅ x) + ((3 ⋅ x) + 20) = 20 (((-1) ⋅ 3) ⋅ x) + ((3 ⋅ x) + 20) = 20
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)
4 (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) = x (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) = x
5 20 = x if 20 = (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) and (((-1) ⋅ 3) ⋅ x) + (4 ⋅ x) = x, then 20 = x

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