Perhaps what is missing is these rules:
AT = A (1)
AF = F (2)
A + T = T (3)
A + F = A (4)
Which can be derived from the given axioms, apparently. I’m not sure if some necessary axioms were omitted.
Using some of these, here’s one way to derive B!A=!A from !B=AD:
!B = AD
!B + A = AD + A
!B + A = AD + AT (1)
!B + A = A(D + T) (Distributivity)
!B + A = AT (3)
!B + A = A (1)
!!B!A = !A (Duality)
B!A = !A
EDIT: The original post now has updated times and links, so refer to that instead.
Here are links to the times suggested, for convenience:
New York City: Fridays at 1pm
Paris: Tuesdays at 1pm
San Francisco: Wednesdays at 1pm
Melbourne: Tuesdays at 9pm (edited to actually coincide with Paris)
I’d suggest posting meeting times using timeanddate.com, to help avoid confusion about time zones and daylight savings.