Transitive Property of Equality Variation 2
Additive Inverse 2
Multiplication Property 2
Multiplicative Identity 3
Remove One
Remove One 2
Division Theorem
Multiply by Inverse 2
Divide by Term
Negative Exponent

Proof: Divide by Term

Let's prove the following theorem:

if the following are true:
  • a = b ⋅ c
  • not (b = 0)

then c = a / b

Proof:

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Given
1 a = b ⋅ c
2 not (b = 0)
Proof Table
# Claim Reason
1 (1 / b) ⋅ a = (1 / b) ⋅ (b ⋅ c) if a = b ⋅ c, then (1 / b) ⋅ a = (1 / b) ⋅ (b ⋅ c)
2 (1 / b) ⋅ (b ⋅ c) = c if not (b = 0), then (1 / b) ⋅ (b ⋅ c) = c
3 (1 / b) ⋅ a = c if (1 / b) ⋅ a = (1 / b) ⋅ (b ⋅ c) and (1 / b) ⋅ (b ⋅ c) = c, then (1 / b) ⋅ a = c
4 (1 / b) ⋅ a = a / b (1 / b) ⋅ a = a / b
5 a / b = c if (1 / b) ⋅ a = a / b and (1 / b) ⋅ a = c, then a / b = c
6 c = a / b if a / b = c, then c = a / b
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