Theorem nexdv

Description: Deduction for generalization rule for negated wff. (Contributed by NM, 5-Aug-1993) Reduce dependencies on axioms. (Revised by Wolf Lammen, 13-Jul-2020) (Proof shortened by Wolf Lammen, 10-Oct-2021)

	Ref	Expression
Hypothesis	nexdv.1	|- ( ph -> -. ps )
Assertion	nexdv	|- ( ph -> -. E. x ps )

Proof

Step	Hyp	Ref	Expression
1		nexdv.1	|- ( ph -> -. ps )
2		ax-5	|- ( ph -> A. x ph )
3	2 1	nexdh	|- ( ph -> -. E. x ps )