What is the difference between the substitution property of equality and the transitive property of equality?
The substitution property of equality states:
If x=y then y can be substituted for x in any expression.
The transitive property of equality states:
If x=y and y=z, then x=z
In the transitive property, you are using the substitution property:
Given: x=y (1)
Given: y=z (2)
Substitute (1) in (2)
The substitution property is more general than the transitive property because one can not only substitute x for y in y=z but on any expression. In other words, the transitive property is only one instance in which the substitution property can be applied.