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Is this the right Conversion?
It is not correct: (GFb & FXb) is not equivalent to F(Gb & Fb); why do you believe that it is so?
A correct computation would be as follows
!A(GXFb & FXb) = !A(GFXb & FXb) = !A(GFXb) = !AGFb = !AGAFb = EFEG!b