To formalize, let:
G = "God exists",
P = "I pray", and
A = "my prayers are answered".
Then, by the premise, we have:
~G --> ~(P --> A) (premise)
~G --> ~(~P \/ A) (def'n of -->)
~G --> (P /\ ~S) (distributing the ~)
~P (given)
~(P /\ ~S) (since ~P)
~(~G) (I forget the name of this property. modus tollens maybe?)
G
Thus, God exists.
|