Solution verification for functional dependency using armstrong axioms

Question

I have the following functional dependencies which includes all attributes of the relation:

{AB -> C, BC -> AD, D -> E, CF -> B}

CF supposedly is a candidate key. The task is: Show that CF is a candidate key given the functional dependencies listed

ACF -> AB (Augmentation)

AB -> C (Follows directly form functional dependencies)

BC -> BAD (Augmentation)

BC -> D (Decomposition)

D -> E (Follows directly from functional dependencies)

This came up as part of an algorithm, which has no name in my script. In line 10 the candidate key {CF} was discovered and I wanted to verify that it is indeed a candidate key.

1. LEFT = {F}
2. NOWHERE = {}
3. MIXED = {ABCD}
4. RIGHT = {E}
5. 2^MIXED = {{}, {A}, {B}, {C}, {D}, {AB}, {AC}, {AD}, {BC}, {BD}, {CD}, {ABC}, {ABD}, {ACD}, {BCD}, {ABCD}}
6. LEFT ∪ NOWHERE = {F}
7. {F}G+ (Closure) = {F}
   2^MIXED = {{A}, {B}, {C}, {D}, {AB}, {AC}, {AD}, {BC}, {BD}, {CD}, {ABC}, {ABD}, {ACD}, {BCD}, {ABCD}}
8. {AF}G+ = {AF}
   2^MIXED = {{B}, {C}, {D}, {AB}, {AC}, {AD}, {BC}, {BD}, {CD}, {ABC}, {ABD}, {ACD}, {BCD}, {ABCD}}
9. {BF}G+ = {BF}
   2 MIXED = {{C}, {D}, {AB}, {AC}, {AD}, {BC}, {BD}, {CD}, {ABC}, {ABD}, {ACD}, {BCD}, {ABCD}}
10. {CF}G+ = {CFBADE} Candidate key!
    2 MIXED = {{D}, {AB}, {AD}, {BD}, {ABD}}
11. {DF}G+ = {DFE}
    2 MIXED = {{AB}, {AD}, {BD}, {ABD}}
12. {ABF}G+ = {ABFCDE} Candidate key!
    2 MIXED = {{AD}, {BD}}
13. {ADF}G+ = {ADFE}
    2 MIXED = {{BD}}
14. {BDF}G+ = {BDFE}
    2 MIXED = {}

I also have no idea why the author choose the description 2^mixed for the combinations of all the attributes