Do you think the transitive property of equality is superfluous when we have the substitution property?
There exists both a transitive property and a substitution property of equality. I think that having both of them is redundant, and I favor the substitution property over the transitive property.
The transitive property of equality states that If a=b & b=c, then a=c.
The substitution property of equality states that if a=b, then a & b can be substituted for each other in any expression.
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It seems as though whenever the transitive property is applied, it is implicitly the substitution property. So, why go out of the way to label it as its own property?
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