Subtraction Example
Subtract Substitute

Proof: Subtract Substitute

Let's prove the following theorem:

if a = b, then x - a = x - b

Proof:

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Given
1 a = b
Proof Table
# Claim Reason
1 x - a = x + (a ⋅ (-1)) x - a = x + (a ⋅ (-1))
2 a ⋅ (-1) = b ⋅ (-1) if a = b, then a ⋅ (-1) = b ⋅ (-1)
3 x + (a ⋅ (-1)) = x + (b ⋅ (-1)) if a ⋅ (-1) = b ⋅ (-1), then x + (a ⋅ (-1)) = x + (b ⋅ (-1))
4 x - a = x + (b ⋅ (-1)) if x - a = x + (a ⋅ (-1)) and x + (a ⋅ (-1)) = x + (b ⋅ (-1)), then x - a = x + (b ⋅ (-1))
5 x + (b ⋅ (-1)) = x - b x + (b ⋅ (-1)) = x - b
6 x - a = x - b if x - a = x + (b ⋅ (-1)) and x + (b ⋅ (-1)) = x - b, then x - a = x - b
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