Theorem nexdh 1792

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

Hypotheses

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

Assertion

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

Proof of Theorem nexdh

Step	Hyp	Ref	Expression
1		nexdh.1	. . 3 |- ( ph -> A. x ph )
2		nexdh.2	. . 3 |- ( ph -> -. ps )
3	1, 2	alrimih 1751	. 2 |- ( ph -> A. x -. ps )
4		alnex 1706	. 2 |- ( A. x -. ps <-> -. E. x ps )
5	3, 4	sylib 208	1 |- ( ph -> -. E. x ps )

Syntax hints:   -. wn 3   -> wi 4   A.wal 1481   E.wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by:  nexdv  1864  nexd  2089  nexdOLD  2198