Theorem nexdv 1929

Description: Deduction for generalization rule for negated wff. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
nexdv.1	|- ( ph -> -. ps )

Assertion

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

Distinct variable group:   ph, x

Allowed substitution hint:   ps( x)

Proof of Theorem nexdv

Step	Hyp	Ref	Expression
1		ax-17 1519	. 2 |- ( ph -> A. x ph )
2		nexdv.1	. 2 |- ( ph -> -. ps )
3	1, 2	nexd 1606	1 |- ( ph -> -. E. x ps )

Syntax hints:   -. wn 3   -> wi 4   E.wex 1485

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 609  ax-in2 610  ax-5 1440  ax-gen 1442  ax-ie2 1487  ax-17 1519

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-fal 1354

This theorem is referenced by:  pw1nct  14036