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Theorem hbn 1776
Description: If x is not free in φ, it is not free in ¬ φ. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 17-Dec-2017.)
Hypothesis
Ref Expression
hbn.1 (φxφ)
Assertion
Ref Expression
hbn φx ¬ φ)

Proof of Theorem hbn
StepHypRef Expression
1 hbnt 1775 . 2 (x(φxφ) → (¬ φx ¬ φ))
2 hbn.1 . 2 (φxφ)
31, 2mpg 1548 1 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:  hba1  1786  hbimOLD  1818  spimehOLD  1821  hbanOLD  1829  hbex  1841  cbv3hvOLD  1851  hbnae  1955  hbnae-o  2179
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