What is the difference between the substitution property of equality and the transitive property of equality?

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flbyrne | (Level 3) Assistant Educator

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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)

Then: x=z

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.