Arm Gcc Weak Alias Redefinition

I wanted to create weak alias for several functions so that I can declare it in a header file but then define it later on in different files. For some reason I still get a redefinition error from gcc.

Ideally for functions that don't have implementations I would like for it to default back on the alias.

I have tried removing alias("Default_Handler") and it seems to compile but it sort of destroys my intention for this application I am trying to write.

vector_table.h

void __attribute__((noreturn))  Default_Handler (void);                                                  
void NMI_Handler(void) __attribute__((weak, alias("Default_Handler"))); 

startup.c

#include "vector_table.h"

void Default_Handler(void){                                                                                                                                
    for(;;);                                                                      
}                                                                               

void NMI_Handler(void){                                                         
    for(;;);                                                                      
}

arm-none-eabi-gcc -mcpu=cortex-m4 -mthumb -mfpu=fpv4-sp-d16 -mfloat-abi=hard -Wall -Wno-unused -Wextra -pedantic -H -g3 -gdwarf-2 -O0 -std=c90 -ffreestanding -c startup.c

startup.c:93:6: error: redefinition of 'NMI_Handler'
 void NMI_Handler(void){
      ^
In file included from startup.c:3:0:
vector_table.h:17:6: note: previous definition of 'NMI_Handler' was here
 void NMI_Handler(void) __attribute__((weak, alias("Default_Handler")));