Theorem nexdh

Description: Deduction for generalization rule for negated wff. (Contributed by NM, 2-Jan-2002)

	Ref	Expression
Hypotheses	nexdh.1	|- ( ph -> A. x ph )
	nexdh.2	|- ( ph -> -. ps )
Assertion	nexdh	|- ( ph -> -. E. x ps )

Proof

Step	Hyp	Ref	Expression
1		nexdh.1	|- ( ph -> A. x ph )
2		nexdh.2	|- ( ph -> -. ps )
3	1 2	alrimih	|- ( ph -> A. x -. ps )
4		alnex	|- ( A. x -. ps <-> -. E. x ps )
5	3 4	sylib	|- ( ph -> -. E. x ps )