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Theorem nalfal 33771
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 1810 . 2 𝑥 ¬ ⊥
2 falim 1555 . . 3 (⊥ → ¬ ∀𝑥 ¬ ⊥)
32sps 2186 . 2 (∀𝑥⊥ → ¬ ∀𝑥 ¬ ⊥)
41, 3mt2 203 1 ¬ ∀𝑥
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wal 1536  wfal 1550
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-12 2179
This theorem depends on definitions:  df-bi 210  df-tru 1541  df-fal 1551  df-ex 1782
This theorem is referenced by: (None)
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