How do you get the guy blocking the Cerulean Cave to let you inside in Pokemon FireRed and LeafGreen?

After beating the Pokemon League, you still can't go to the Cerulean Cave. To be able to enter you have to get the National Dex by catching 60 different types of Pokemon and showing your PokeDex to Professor Oak, also you have to do the Ruby Sapphire side quest in the Sevii Islands and beat the Pokemon League once more when their Pokemon are stronger and different. By then you will be able to enter the Cerulean Cave that contains Pokemon levels 50-60 and Mewtwo Level 70 at the Bottom floor of the Dungeon.