Proof: Transitive Property of Equality Variation 1
Let's prove the following theorem:
if the following are true:
- a = c
- b = c
then a = b
This theorem is very similar to the Transitive Property of Equality. The only difference is that the terms on the second condition are switched.
We begin the proof by listing any givens or assumptions, which are statements that we can assume are true.
Each row in the proof table contains a claim, which is a statement that can be derived from properties, givens, and other derived statements. The reason tells us how or why we were able to make the claim.
Proof:
Given
| 1 | a = c |
|---|---|
| 2 | b = c |
| # | Claim | Reason |
|---|---|---|
| 1 | c = b | if b = c, then c = b |
| 2 | a = b | if c = b and a = c, then a = b |
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