Dado ∀ x {\displaystyle \forall _{x}} ¬ {\displaystyle \lnot } Q(x) y ∀ x {\displaystyle \forall _{x}} (P(x) ⇒ {\displaystyle \Rightarrow } Q(x)) demostrar que ∀ x {\displaystyle \forall _{x}} ¬ {\displaystyle \lnot } P(x)
1. ∀ x {\displaystyle \forall _{x}} ¬ {\displaystyle \lnot } Q(x) premisa
2. ¬ {\displaystyle \lnot } Q(x) S x x {\displaystyle S_{x}^{x}} particularizacion 1.
3. ∀ x {\displaystyle \forall _{x}} (P(x) ⇒ {\displaystyle \Rightarrow } Q(x)) premisa
4.P(x) ⇒ {\displaystyle \Rightarrow } Q(x) S x x {\displaystyle S_{x}^{x}} particularizacion 3.
5. ¬ {\displaystyle \lnot } P(x) modus tollens 2. 4.
6. ∀ x {\displaystyle \forall _{x}} ¬ {\displaystyle \lnot } P(x) generalizacion del universal
