Theorem nalfal 36716

Description: Not all sets hold ⊥ as true. (Contributed by Anthony Hart, 13-Sep-2011.)

Assertion

Ref	Expression
nalfal	⊢ ¬ ∀𝑥⊥

Proof of Theorem nalfal

Step	Hyp	Ref	Expression
1		alfal 1827	. 2 ⊢ ∀𝑥 ¬ ⊥
2		falim 1576	. . 3 ⊢ (⊥ → ¬ ∀𝑥 ¬ ⊥)
3	2	sps 2219	. 2 ⊢ (∀𝑥⊥ → ¬ ∀𝑥 ¬ ⊥)
4	1, 3	mt2 202	1 ⊢ ¬ ∀𝑥⊥

Syntax hints:  ¬ wn 3  ∀wal 1557  ⊥wfal 1571

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-12 2211

This theorem depends on definitions:  df-bi 209  df-tru 1562  df-fal 1572  df-ex 1799

This theorem is referenced by: (None)