Theorem nexdv 1852

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 1459	. 2 |- ( ph -> A. x ph )
2		nexdv.1	. 2 |- ( ph -> -. ps )
3	1, 2	nexd 1544	1 |- ( ph -> -. E. x ps )

Syntax hints:   -. wn 3   -> wi 4   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  ax-17 1459

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

This theorem is referenced by: (None)