I am working on the following exercise: $$ (\exists a \in M_1:A_1(a))\Rightarrow(\exists b \in M_2:A_2(b)) \equiv \exists b \in M_2 \exists a \in M_1:(A_1(a) \Rightarrow A_2(b)) $$
I have been working on this for a while now however, I am always stuck at a certain point. From whichever angle I approach the problem, I simply won't get forward. (working from left to right)
This is where I am stuck: $$ \exists a \in M_2 :(\forall a\in M_1:(A_1(a) \Rightarrow A_2(b))) $$ Tips are highly appreciated. Thanks in advance.
Edit: The equivalence is wrong!
$$ (\exists a \in M_1:A_1(a))\Rightarrow(\exists b \in M_2:A_2(b)) \\ \equiv (\neg\exists a \in M_1:A_1(a))\vee(\exists b \in M_2:A_2(b))\\ \equiv \exists b \in M_2:[(\neg\exists a \in M_1:A_1(a))\vee(A_2(b))]\\ \equiv \exists b \in M_2:[(\forall a \in M_1:\neg A_1(a))\vee A_2(b)]\\ \equiv \exists b \in M_2:\forall a \in M_1:[\neg A_1(a)\vee A_2(b)]\\ \equiv \exists b \in M_2:\forall a \in M_1:[ A_1(a)\Rightarrow A_2(b)]\\ \not\equiv \exists b \in M_2:\exists a \in M_1:[A_1(a) \Rightarrow A_2(b)] $$