How do I prove the following lemma of propostional logic:
$(A_1 \vee \ldots \vee A_k) \wedge (A_1 \rightarrow B) \wedge \ldots \wedge (A_k \rightarrow B) \vDash B$
I tried proving it with induction. The base case k = 1 is fairly easy to prove. Unfortunately I sturggle proving the induction step. Maybe its not the right approach?