Lifetime requirements for storage of std::exception_ptr

Given the example about std::exception_ptr from cpprefernce.com, would it be legal to shorten the code in the following way? If all the handling is done inside the catch-block, there should be no need to store the std::exception_ptr at an outer or even at global scope.

#include <iostream>
#include <string>
#include <exception>
#include <stdexcept>

void handle_eptr(std::exception_ptr eptr) // passing by value is ok
{
    try {
        if (eptr) {
            std::rethrow_exception(eptr);
        }
    } catch(const std::exception& e) {
        std::cout << "Caught exception \"" << e.what() << "\"\n";
    }
}

int main()
{
    try {
        std::string().at(1); // this generates an std::out_of_range
    } catch(...) {
        handle_eptr(std::current_exception()); // CHANGE: HANDLING THE std::exception_ptr AS R-VALUE INSIDE THE CATCH BLOCK
    }
} // destructor for std::out_of_range called here, when the eptr is destructed