G --> (P --> A) is not logically equivalent to ~G --> ~(P --> A)
For example:
"If I am sleepy, then I will sleep"
S = "I am Sleepy"
W = "Will Sleep"
S --> W
But let's throw in "If I am bored, then I will sleep"
B = "I am bored"
B --> W
Since both B and S imply W, you cannot say ~S --> ~W because you're really saying
(~S)(B) ^ (~S)(~B) --> ~W, which is not true.
This is why you first need to prove that prayers are only answered by God
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