Rules of Inference & Equivalency in Predicate Logic

Together We'll Review Some Rules of Inference and Equivalency in Predicate Logic:

(1) Universal Instantiation (UI). . .
Premise: (Ɐx)(Fx)
Inference: Fy or Fa

(2) Existential Instantiation (EI). . .
Premise: (Ǝx)(Fx)
Inference: Fa
(Note: The constant "a" cannot have been used earlier in proof.)

(3) Universal Generalization (UG). . .
Premise: Fy
Inference: (Ɐx)(Fx)
(Note: The variable "y" cannot be a constant.)

(4) Existential Generalization (EG). . .
Premise: Fa
Inference: (Ǝx)(Fx)
Premise: Fy
Inference: (Ǝx)(Fx)

(5) Quantifier Negation (QN) . . .
(Ɐx)(Fx) ≡ ¬(Ǝx)(¬Fx)
¬(Ɐx)(Fx) ≡ (Ǝx)(¬Fx)
(Ǝx)(Fx) ≡ ¬(Ɐx)(¬Fx)
¬(Ǝx)(Fx) ≡ (Ɐx)( ¬Fx)

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