Theorem nexd

Description: Deduction for generalization rule for negated wff. (Contributed by Mario Carneiro, 24-Sep-2016)

	Ref	Expression
Hypotheses	nexd.1	|- F/ x ph
	nexd.2	|- ( ph -> -. ps )
Assertion	nexd	|- ( ph -> -. E. x ps )

Proof

Step	Hyp	Ref	Expression
1		nexd.1	|- F/ x ph
2		nexd.2	|- ( ph -> -. ps )
3	1	nf5ri	|- ( ph -> A. x ph )
4	3 2	nexdh	|- ( ph -> -. E. x ps )