Theorem nexd 1592

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

Hypotheses

Ref	Expression
nexd.1	|- ( ph -> A. x ph )
nexd.2	|- ( ph -> -. ps )

Assertion

Ref	Expression
nexd	|- ( ph -> -. E. x ps )

Proof of Theorem nexd

Step	Hyp	Ref	Expression
1		nexd.1	. . 3 |- ( ph -> A. x ph )
2		nexd.2	. . 3 |- ( ph -> -. ps )
3	1, 2	alrimih 1445	. 2 |- ( ph -> A. x -. ps )
4		alnex 1475	. 2 |- ( A. x -. ps <-> -. E. x ps )
5	3, 4	sylib 121	1 |- ( ph -> -. E. x ps )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1329   E.wex 1468

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-5 1423  ax-gen 1425  ax-ie2 1470

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337

This theorem is referenced by:  nexdv  1906