Verification / Correction of a logic expression

[QCastro]

Hello, could someone tell me if the expression below is correct?
[tex]\exists[/tex]c [tex]\in[/tex] X \cap Y [tex]\iff[/tex] {c [tex]\mid[/tex] M(c) [tex]\colon[/tex] X [tex]\Rightarrow[/tex] Y [tex]\vee[/tex] Y [tex]\Rightarrow[/tex] X}

What I want to say is: 'c' exists and belongs to X and Y (an intersection), if and only if c exists that satisfy the function M(c) which is valid only if X stands for Y or Y stands for X

[Guest]

I don't understand what a function being "valid only if X stands for Y and Y stands for X" means. I presume that "X stands for Y and Y stands for X" means that X= Y- that "X" and "Y" are names for the same set.