Theorem nexd 1544

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 1398	. 2 |- ( ph -> A. x -. ps )
4		alnex 1428	. 2 |- ( A. x -. ps <-> -. E. x ps )
5	3, 4	sylib 120	1 |- ( ph -> -. E. x ps )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1282   E.wex 1421

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577  ax-5 1376  ax-gen 1378  ax-ie2 1423

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-fal 1290

This theorem is referenced by:  nexdv  1852