Im terrible at proofs....

Use the definition of conditional probabilities to prove that any events A, B, C, D, E and F,

P(A$\displaystyle \cap$B$\displaystyle \cap$C$\displaystyle \cap$D$\displaystyle \cap$E$\displaystyle \cap$F) = P(A$\displaystyle \cap$B$\displaystyle \cap$C$\displaystyle \cap$D$\displaystyle \mid$E$\displaystyle \cap$F)P(E$\displaystyle \cap$F)

and P(A$\displaystyle \cap$B$\displaystyle \cap$C$\displaystyle \cap$D$\displaystyle \cap$E$\displaystyle \cap$F) = P(A$\displaystyle \cap$B$\displaystyle \mid$C$\displaystyle \cap$D$\displaystyle \cap$E$\displaystyle \cap$F)P(C$\displaystyle \cap$D$\displaystyle \cap$E$\displaystyle \mid$F)P(F)

Also, can anyone form a similar identity?