Let $\Gamma$ be any set of formulas of P. Show that the following are equivalent:
(1) $\Gamma$ is consistent and complete.
(2) There is exactly one truth assignment that satisfies $\Gamma$
I have proved from (2) to (1).
But from (1) to (2), so far (1) can prove that for any truth assignment $\phi$, then $\phi(A)=T$. But how should we prove there is only one truth assignment?