Chapter 1.6, Problem 23E

Identify the error or errors in argument that supposedly shows that if (

$\exists xP\left(x\right)\wedge \exists xQ\left(x\right)$ is true then $\exists x\left(P\left(x\right)\wedge Q\left(x\right)\right)$ is true.

1. $\exists xP\left(x\right)\wedge \exists xQ\left(x\right)$ Premise

2. $\exists xP\left(x\right)$ Simplification from (1)

3. $P\left(c\right)$ Existential instantiation from (2)

4. $\exists xQ\left(x\right)$ Simplification from (1)

5. $Q\left(c\right)$ Existential instantiation from (4)

6. $P\left(x\right)\wedge Q\left(c\right)$ Conjunction from (3) and (5)

7. $\exists x\left(P\left(x\right)\wedge Q\left(x\right)\right)$ Existential generalization