Theorem nexdv 1946

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 1536	. 2 |- ( ph -> A. x ph )
2		nexdv.1	. 2 |- ( ph -> -. ps )
3	1, 2	nexd 1623	1 |- ( ph -> -. E. x ps )

Syntax hints:   -. wn 3   -> wi 4   E.wex 1502

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-5 1457  ax-gen 1459  ax-ie2 1504  ax-17 1536

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-fal 1369

This theorem is referenced by:  pw1nct  15024