Theorem nexdv 1326

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-17 971	. 2 |- (ph -> A.xph)
2		nexdv.1	. 2 |- (ph -> -. ps)
3	1, 2	nexd 1102	1 |- (ph -> -. E.xps)

Syntax hints:  -. wn 2   -> wi 3  E.wex 980

This theorem is referenced by:  sbc2or 1958  relimasn 3425  fvprc 3721  fvopabn 3786  genpnnp 5108  dffsum 6998  dfisum 7191  efilcp 10572  efilcpOLD 10573  efilcp2 10581  efilcp2OLD 10582

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-17 971  ax-4 973  ax-5o 975

This theorem depends on definitions:  df-bi 147  df-ex 981

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