TITLE: If we accept a false statement, can we prove anything?
QUESTION [6 upvotes]: I think that the question is contained in the title.
Suppose we begin from something that is false for example $1=0$.
Is it possible using only $\Rightarrow$ (and of course $\lnot ,\wedge,\lor$)  to prove any possible statement?
It has been ages since i studied logic at the university so i would prefer a simple explanation
(if possible)

REPLY [5 votes]: You can use a truth table to prove that $P\implies [\neg P\implies Q]$. 
In words, if we know that $P$ is true, but we assume, for the sake of argument, that $P$ is false (i.e. $\neg P)$, then any proposition $Q$ can be derived.
We can also prove this theorem as follows:

Suppose $P$
Suppose $\neg P$
Suppose $\neg Q$
We obtain the contradiction $P\land \neg P$
Therefore, we must have $\neg\neg Q$, or equivalently $Q$
Therefore, $\neg P \implies Q$
Therefore, $P\implies [\neg P\implies Q]$