If you are so confident in 1=1... Then you clearly believe it is true. You also have to trust your justifications for proving it (IE: by definition) are true. Essentially you just took a quick blink of faith when you considered 1=1 to be true 
As the non-existence thread was showed: you cannot be truly certain of anything. In my mind, you can prove that 1=1 is true, and can based everything in and outside of the universe around that fact. Just like you can in my mind prove that there is no pony dancing on this table.
All the evidence screams that there is no pony and that 1=1 is true... but we still have to take it on a little bit of faith

As the non-existence thread was showed: you cannot be truly certain of anything. In my mind, you can prove that 1=1 is true, and can based everything in and outside of the universe around that fact. Just like you can in my mind prove that there is no pony dancing on this table.
All the evidence screams that there is no pony and that 1=1 is true... but we still have to take it on a little bit of faith

Please give me a home where cloud buffalo roam
Where the dear and the strangers can play
Where sometimes is heard a discouraging word
But the skies are not stormy all day