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Theorem nalf 32739
Description: Not all sets hold as true. (Contributed by Anthony Hart, 13-Sep-2011.)
Assertion
Ref Expression
nalf ¬ ∀𝑥

Proof of Theorem nalf
StepHypRef Expression
1 alnof 32738 . 2 𝑥 ¬ ⊥
2 falim 1646 . . 3 (⊥ → ¬ ∀𝑥 ¬ ⊥)
32sps 2209 . 2 (∀𝑥⊥ → ¬ ∀𝑥 ¬ ⊥)
41, 3mt2 191 1 ¬ ∀𝑥
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wal 1629  wfal 1636
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-12 2203
This theorem depends on definitions:  df-bi 197  df-tru 1634  df-fal 1637  df-ex 1853
This theorem is referenced by: (None)
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