statement 1: $Γ$ is satisfiable implies $Γ$ is consistent.

statement 2: If $Γ$ derives $α$ then $Γ$ entails $α$.

I can easily prove statement 1 from 2 , but not 2 from 1 (without using strong completeness theorem).

  • $\begingroup$ Try: $\Gamma$ entails $\alpha$ iff $\Gamma \land \lnot \alpha$ is unsatisfiable, $\Gamma$ derives $\alpha$ iff $\Gamma \land \lnot \alpha$ is inconsistent. $\endgroup$ – Yuval Filmus Nov 25 '19 at 17:47

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