Theorem nalfal 34592

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 1811	. 2 ⊢ ∀𝑥 ¬ ⊥
2		falim 1556	. . 3 ⊢ (⊥ → ¬ ∀𝑥 ¬ ⊥)
3	2	sps 2178	. 2 ⊢ (∀𝑥⊥ → ¬ ∀𝑥 ¬ ⊥)
4	1, 3	mt2 199	1 ⊢ ¬ ∀𝑥⊥

Syntax hints:  ¬ wn 3  ∀wal 1537  ⊥wfal 1551

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-12 2171

This theorem depends on definitions:  df-bi 206  df-tru 1542  df-fal 1552  df-ex 1783

This theorem is referenced by: (None)