If the goal is to apply a symbolic code transformation that generates a composite pure function from a list of individual pure functions, then `Distribute` can be used:

```
cons = {con1[#]&, con2[#]&, con3[#]&}

Distribute[And @@ cons, Function, And]

(* con1[#1] && con2[#1] && con3[#1] & *)
```

But if the goal is to simply evaluate the functions and determine if they all return true, then the other answers involving `AllTrue`, `Through`, `ComapApply`, etc. are more appropriate.