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Theorem nalfal 33648
Description: Not all sets hold as true. (Contributed by Anthony Hart, 13-Sep-2011.)
Assertion
Ref Expression
nalfal ¬ ∀𝑥

Proof of Theorem nalfal
StepHypRef Expression
1 alfal 1800 . 2 𝑥 ¬ ⊥
2 falim 1545 . . 3 (⊥ → ¬ ∀𝑥 ¬ ⊥)
32sps 2174 . 2 (∀𝑥⊥ → ¬ ∀𝑥 ¬ ⊥)
41, 3mt2 201 1 ¬ ∀𝑥
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wal 1526  wfal 1540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-12 2167
This theorem depends on definitions:  df-bi 208  df-tru 1531  df-fal 1541  df-ex 1772
This theorem is referenced by: (None)
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