Theorem nexdv 1328

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:   ph,x

Proof of Theorem nexdv

Step	Hyp	Ref	Expression
1		ax-17 973	. 2 |- (ph -> A.xph)
2		nexdv.1	. 2 |- (ph -> -. ps)
3	1, 2	nexd 1104	1 |- (ph -> -. E.xps)

Syntax hints:  -. wn 2   -> wi 3  E.wex 982

This theorem is referenced by:  sbc2or 1961  relimasn 3431  fvprc 3727  fvopabn 3792  genpnnp 5120  dffsum 6998  dfisum 7191  efilcp 10556  efilcp2 10561

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-17 973  ax-4 975  ax-5o 977

This theorem depends on definitions:  df-bi 147  df-ex 983

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