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Theorem hbnt 1775
Description: Closed theorem version of bound-variable hypothesis builder hbn 1776. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
hbnt (x(φxφ) → (¬ φx ¬ φ))

Proof of Theorem hbnt
StepHypRef Expression
1 ax6o 1750 . . 3 x ¬ xφφ)
21con1i 121 . 2 φx ¬ xφ)
3 con3 126 . . 3 ((φxφ) → (¬ xφ → ¬ φ))
43al2imi 1561 . 2 (x(φxφ) → (x ¬ xφx ¬ φ))
52, 4syl5 28 1 (x(φxφ) → (¬ φx ¬ φ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-ex 1542
This theorem is referenced by:  hbn  1776  19.9ht  1778  nfnd  1791  nfimdOLD  1809  hbnd  1883
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