Proving that $a⊢b$ if and only if $a⇒b$ is a tautology

On my university exam paper there was a problem which description was the following:

Prove the following assertion: $$a⊢b$$ if and only if $$a⇒b$$ is a tautology.

How can I prove it?

• What have you tried ? – Mauro ALLEGRANZA Jan 5 at 8:55
• What is your proof system ? – Mauro ALLEGRANZA Jan 5 at 8:55
• – Mauro ALLEGRANZA Jan 5 at 8:56
• @MauroALLEGRANZA What do you mean what is my proof system? – Dimitris Prasakis Jan 5 at 9:40
• What does it mean for you "$a \vdash b$" ? – Mauro ALLEGRANZA Jan 5 at 9:52