Proof: Substitute 7

Let's prove the following theorem:

if the following are true:
  • a + (b ⋅ (-1)) = c
  • b = d

then a + (d ⋅ (-1)) = c

Proof:

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Given
1 a + (b ⋅ (-1)) = c
2 b = d
Proof Table
# Claim Reason
1 a + (b ⋅ (-1)) = a + (d ⋅ (-1)) if b = d, then a + (b ⋅ (-1)) = a + (d ⋅ (-1))
2 a + (d ⋅ (-1)) = c if a + (b ⋅ (-1)) = c and a + (b ⋅ (-1)) = a + (d ⋅ (-1)), then a + (d ⋅ (-1)) = c

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