Theorem nexdv 983

Description: Deduction for generalization rule for negated wff.

Hypothesis

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

Assertion

Ref	Expression
nexdv	|- (ph -> -. E.xps)

Distinct variable group(s):   ph,x

Proof of Theorem nexdv

Step	Hyp	Ref	Expression
1		ax-17 925	. 2 |- (ph -> A.xph)
2		nexdv.1	. 2 |- (ph -> -. ps)
3	1, 2	nexd 780	1 |- (ph -> -. E.xps)

Syntax hints:  -. wn 1   -> wi 2  E.wex 678

This theorem is referenced by:  sbc2or 1454  imasn 2616  fvprc 2829  genpnnp 3902

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-gen 677  ax-17 925

This theorem depends on definitions:  df-bi 128  df-ex 679

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