Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Perhaps I'm just too tired, but is it valid to say $(A=B \iff B=C) \implies (A=C)$ ? If so, what justifies it?

The thing is, by assuming just $(A=B \iff B=C)$ I don't see how we reach $A=C$, for I would also need $A=B$ or $B=C$ for hypothesis.

Thanks in advance for any clarification.

share|cite|improve this question
Hint: What happens if all the three $A,B,C$ are pairwise distinct? – Tobias Kildetoft Sep 11 '13 at 18:39
@zerosofthezeta: $A=B,B=C$ is not the same as $A=B\iff B=C$. – abiessu Sep 11 '13 at 18:46
up vote 2 down vote accepted

No this is not true. What you might conclude is that $(A=B \implies B = C)\implies ((A=B)\implies A = C)$ and going the other way $(A=B \Longleftarrow B = C)\implies ((B=C)\implies A = C)$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.