The only thing you have to do after setting up the validations is to call a method that will validate the errors. So follow below:
<button @click="validate">Submit</button>
The method:
validate () {
this.$v.$touch() //it will validate all fields
if (!this.$v.$invalid) { //invalid, becomes true when a validations return false
//you dont have validation error.So do what u want to do here
}
}