What is the relation A = B = C called in a proof?
When writing a proof if I have the relationship $$ A = B = C $$
And I want to use that to prove $$ A = C $$
I remember there being some term for it. What is that term, and what would be an appropriate intertext in this situation?
$\endgroup$ 13 Answers
$\begingroup$What you're looking for is the transitive property of equality.
$$ \text{Given}\\ A = B\\ B = C\\ \text{Equality is transitive}\\ \therefore A = C $$
$\endgroup$ $\begingroup$Transitivity is the word you're looking for.
$\endgroup$ $\begingroup$" $A=B, \ B=C \implies A=C$ " is called transitivity of equality.
$\endgroup$
